Edit Profile (opens in new tab) Chen, Bang-Yen Compute Distance To: Compute Author ID: chen.bang-yen Published as: Chen, Bang-Yen; Chen, Bang-yen; Chen, B.-Y.; Chen, B. Y.; Chen, B.-y.; Chen, Bang Yen; Chen, Bang-Yeng more...less External Links: MGP · Wikidata · ResearchGate · GND · IdRef Documents Indexed: 547 Publications since 1967, including 14 Books 3 Contributions as Editor Reviewing Activity: 326 Reviews Biographic References: 6 Publications Co-Authors: 85 Co-Authors with 256 Joint Publications 1,187 Co-Co-Authors all top 5 Co-Authors 292 single-authored 31 Dillen, Franki 29 Verstraelen, Leopold C. A. 25 Vrancken, Luc 20 Yano, Kentaro 16 Deshmukh, Sharief 16 Ogiue, Koichi 10 Morvan, Jean-Marie 10 Van der Veken, Joeri 10 Vanhecke, Lieven 9 Garay, Oscar Jesus 9 Lue, Huei-Shyong 8 Barros, Manuel 8 Houh, Chorng-Shi 8 Verheyen, Paul 7 Wei, Shihshu Walter 6 Al-Solamy, Falleh Rijaullah 6 Nagano, Tadashi 6 Siraj-Uddin 5 Deprez, Johan 5 Ludden, Gerald D. 5 Mihai, Ion 5 Vîlcu, Gabriel Eduard 4 Blair, David E. 4 Li, Shijie 3 Alghanemi, Azeb 3 Alodan, Haila 3 Ishikawa, Susumu 3 Kuan, Wei-Eihn 3 Maeda, Sadahiro 3 Mihai, Adela 3 Munteanu, Marian-Ioan 3 Piccinni, Paolo 3 Song, Hongzao 3 Tazawa, Yoshihiko 2 Al-Jedani, Awatif 2 Baikoussis, Christos 2 Fastenakels, Johan 2 Kim, Youngho 2 Nore, Thérèse 2 Petrovic, Mira 2 Shahid, Mohammed Hasan 2 Suceavă, Bogdan Dragos 2 Tanaka, Makiko Sumi 2 Turki, Nasser Bin 2 Yamaguchi, Seiichi 1 Alegre, Pablo 1 Alghamdi, Fatimah 1 Alshammari, Sana Hamoud 1 Arslan, Kadri 1 Blaga, Adara-Monica 1 Borrelli, Vincent 1 Brubaker, Nicholas D. 1 Camci, Çetin 1 Carriazo, Alfonso 1 Castro, Ildefonso 1 Chen, Pi-Mei 1 Choi, Miekyung 1 Decu, Simona 1 Defever, Filip 1 Fu, Yu 1 İlarslan, Kazim 1 Jiang, Sheng 1 Kim, Dongsoo S. 1 Kocaman, E. S. 1 Martín-Molina, Verónica 1 Montiel, Sebastián 1 Murathan, Cengizhan 1 Ochiai, Takushiro 1 Oh, Yun Myung 1 Okumura, Masafumi 1 Ou, Ye-Lin 1 Pérez Jiménez, Juan de Dios 1 Prieto-Martín, Alicia 1 Sakai, Takashi 1 Sarabia, Alfonso Sarabia 1 Tamaru, Hiroshi 1 Teng, Th. 1 Teng, Tsing-Houa 1 Uçum, Ali 1 Urbano, Francisco 1 Vajiac, Mihaela B. 1 Vîlcu, Alina Daniela 1 Wang, Xianfeng 1 Wu, Baoqiang 1 Yang, Dan 1 Yang, Jie 1 Yildirim, Handan 1 Zhou, Zhengfang all top 5 Serials 19 Proceedings of the American Mathematical Society 17 Tamkang Journal of Mathematics 17 Soochow Journal of Mathematics 16 International Electronic Journal of Geometry 12 Bulletin of the Institute of Mathematics. Academia Sinica 12 Taiwanese Journal of Mathematics 11 Results in Mathematics 11 Kodai Mathematical Seminar Reports 10 Archiv der Mathematik 10 Comptes Rendus de l’Académie des Sciences. Série I 9 Bulletin of the Australian Mathematical Society 9 Geometriae Dedicata 9 Journal of Differential Geometry 9 Kragujevac Journal of Mathematics 8 Houston Journal of Mathematics 8 Journal of Mathematical Analysis and Applications 8 Journal of Geometry and Physics 8 Journal of Geometry 8 Kodai Mathematical Journal 8 Tôhoku Mathematical Journal. Second Series 7 Journal of the Mathematical Society of Japan 7 Monatshefte für Mathematik 7 Bulletin of the American Mathematical Society 6 Beiträge zur Algebra und Geometrie 6 Glasgow Mathematical Journal 6 Journal of the London Mathematical Society. Second Series 6 Differential Geometry and its Applications 6 Atti della Accademia Nazionale dei Lincei. Serie Ottava. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali 5 Journal of Mathematical Physics 5 Mathematical Proceedings of the Cambridge Philosophical Society 5 Indiana University Mathematics Journal 5 Nagoya Mathematical Journal 5 Proceedings of the Japan Academy. Series A 5 Publicationes Mathematicae Debrecen 5 Tensor. New Series 5 Annals of Global Analysis and Geometry 5 Turkish Journal of Mathematics 4 Israel Journal of Mathematics 4 Annali di Matematica Pura ed Applicata. Serie Quarta 4 Chinese Journal of Mathematics 4 Japanese Journal of Mathematics. New Series 4 Michigan Mathematical Journal 4 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 4 Proceedings of the Edinburgh Mathematical Society. Series II 4 Tokyo Journal of Mathematics 4 Annales de la Faculté des Sciences de Toulouse. Série V. Mathématiques 4 Bulletin de la Société Matheḿatique de Belgique. Série B 4 Kyushu Journal of Mathematics 4 Arab Journal of Mathematical Sciences 4 Balkan Journal of Geometry and its Applications (BJGA) 3 American Journal of Mathematics 3 Duke Mathematical Journal 3 Hokkaido Mathematical Journal 3 Journal of the Korean Mathematical Society 3 Mathematische Annalen 3 Mathematical Journal of Okayama University 3 Nanta Mathematica 3 Transactions of the American Mathematical Society 3 Tsukuba Journal of Mathematics 3 Comptes Rendus Mathématiques de l’Académie des Sciences 3 Bulletin of the Korean Mathematical Society 3 Acta Mathematica Hungarica 3 International Journal of Mathematics 3 Journal of the Australian Mathematical Society. Series A 3 Algebras, Groups and Geometries 3 Mediterranean Journal of Mathematics 3 Bollettino della Unione Matematica Italiana. Series V. A 3 Soochow Journal of Mathematics and Natural Sciences 2 Rocky Mountain Journal of Mathematics 2 Annales Polonici Mathematici 2 Colloquium Mathematicum 2 International Journal of Mathematics and Mathematical Sciences 2 Osaka Journal of Mathematics 2 The Quarterly Journal of Mathematics. Oxford Second Series 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 Bulletin of the Belgian Mathematical Society - Simon Stevin 2 Rendiconti del Seminario Matematico di Messina. Serie II 2 Serdica Mathematical Journal 2 Acta Mathematica Sinica. English Series 2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 Central European Journal of Mathematics 2 International Journal of Geometric Methods in Modern Physics 2 Journal of Geometry and Symmetry in Physics 2 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 2 Series in Pure Mathematics 2 Journal of Advanced Mathematical Studies 2 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 2 Bulletin of the Transilvania University of Brașov. Series III. Mathematics, Informatics, Physics 1 American Mathematical Monthly 1 Classical and Quantum Gravity 1 Computer Methods in Applied Mechanics and Engineering 1 General Relativity and Gravitation 1 Applied Mathematics and Computation 1 Archivum Mathematicum 1 Atti della Accademia Peloritana dei Pericolanti. Classe di Scienze Fisiche, Matemàtiche e Naturali 1 Canadian Journal of Mathematics 1 The Formosan Science 1 Journal für die Reine und Angewandte Mathematik 1 Kyungpook Mathematical Journal 1 Mathematische Nachrichten ...and 22 more Serials all top 5 Fields 526 Differential geometry (53-XX) 37 Global analysis, analysis on manifolds (58-XX) 19 Several complex variables and analytic spaces (32-XX) 15 Algebraic geometry (14-XX) 13 Relativity and gravitational theory (83-XX) 13 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 11 Manifolds and cell complexes (57-XX) 10 Partial differential equations (35-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 5 Convex and discrete geometry (52-XX) 4 History and biography (01-XX) 4 Quantum theory (81-XX) 3 Algebraic topology (55-XX) 3 Operations research, mathematical programming (90-XX) 2 General and overarching topics; collections (00-XX) 2 Topological groups, Lie groups (22-XX) 2 Potential theory (31-XX) 2 Dynamical systems and ergodic theory (37-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Real functions (26-XX) 1 Ordinary differential equations (34-XX) 1 Difference and functional equations (39-XX) 1 Integral transforms, operational calculus (44-XX) 1 General topology (54-XX) 1 Numerical analysis (65-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) 1 Astronomy and astrophysics (85-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 437 Publications have been cited 5,504 times in 2,155 Documents Cited by ▼ Year ▼ Geometry of submanifolds. Zbl 0262.53036Chen, Bang-yen 201 1973 Some pinching and classification theorems for minimal submanifolds. Zbl 0811.53060Chen, Bang-Yen 149 1993 Total mean curvature and submanifolds of finite type. Zbl 0537.53049Chen, Bang-Yen 147 1984 Geometry of slant submanifolds. Zbl 0716.53006Chen, Bang-Yen 143 1990 Geometry of warped product CR-submanifolds in Kaehler manifolds. Zbl 0996.53044Chen, Bang-Yen 135 2001 Some open problems and conjectures on submanifolds of finite type. Zbl 0749.53037Chen, Bang-Yen 130 1991 Slant immersions. Zbl 0677.53060Chen, Bang-Yen 122 1990 On totally real submanifolds. Zbl 0286.53019Chen, Bang-Yen; Ogiue, Koichi 111 1974 Geometry of warped product CR-submanifolds in Kaehler manifolds. II. Zbl 0996.53045Chen, Bang-Yen 87 2001 Pseudo-Riemannian geometry, \(\delta\)-invariants and applications. Zbl 1245.53001Chen, Bang-Yen 86 2011 When does the position vector of a space curve always lie in its rectifying plane? Zbl 1035.53003Chen, Bang-Yen 84 2003 A report on submanifolds of finite type. Zbl 0867.53001Chen, Bang-Yen 73 1996 Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimensions. Zbl 0962.53015Chen, Bang-Yen 66 1999 Totally geodesic submanifolds of symmetric spaces. II. Zbl 0384.53024Chen, Bang-Yen; Nagano, Tadashi 63 1978 Biharmonic surfaces in pseudo-Euclidean spaces. Zbl 0757.53009Chen, Bang-Yen; Ishikawa, Susumu 62 1991 Biharmonic pseudo-Riemannian submanifolds in pseudo-Euclidean spaces. Zbl 0892.53012Chen, Bang-Yeng; Ishikawa, Susumu 60 1998 Geometry of submanifolds and its applications. Zbl 0474.53050Chen, Bang-yen 59 1981 Geometry of warped product submanifolds: a survey. Zbl 1301.53049Chen, Bang-Yen 58 2013 Differential geometry of warped product manifolds and submanifolds. Zbl 1390.53001Chen, Bang-Yen 57 2017 Mean curvature and shape operator of isometric immersions in real-space-forms. Zbl 0866.53038Chen, Bang-Yen 56 1996 Warped product bi-slant immersions in Kaehler manifolds. Zbl 1369.53039Uddin, Siraj; Chen, Bang-Yen; Al-Solamy, Falleh R. 56 2017 Some conformal invariants of submanifolds and their applications. Zbl 0321.53042Chen, Bang-yen 49 1974 Hypersurfaces of a conformally flat space. Zbl 0257.53027Chen, Bang-Yen; Yano, Kentaro 48 1972 Differential geometry of geodesic spheres. Zbl 0503.53013Chen, Bang-Yen; Vanhecke, Lieven 48 1981 Some new obstructions to minimal and Lagrangian isometric immersions. Zbl 1026.53009Chen, Bang-Yen 47 2000 Pointwise slant submanifolds in almost Hermitian manifolds. Zbl 1269.53059Chen, Bang-Yen; Garay, Oscar J. 46 2012 CR-submanifolds of a Kähler manifold. I. Zbl 0431.53048Chen, Bang-yen 45 1981 Rectifying curves as centrodes and extremal curves. Zbl 1082.53012Chen, Bang-Yen; Dillen, Franki 45 2005 A simple characterization of generalized Robertson-Walker spacetimes. Zbl 1308.83159Chen, Bang-Yen 43 2014 Submanifolds with finite type Gauss map. Zbl 0672.53044Chen, Bang-Yen; Piccinni, Paolo 43 1987 On CR-submanifolds of Hermitian manifolds. Zbl 0453.53018Blair, David E.; Chen, Bang-Yen 41 1979 Riemannian geometry of Lagrangian submanifolds. Zbl 1002.53053Chen, Bang-Yen 39 2001 On isometric minimal immersions from warped products into real space forms. Zbl 1022.53022Chen, Bang-Yen 38 2002 Biharmonic ideal hypersurfaces in Euclidean spaces. Zbl 1260.53017Chen, Bang-Yen; Munteanu, Marian Ioan 38 2013 A Riemannian geometric invariant and its applications to a problem of Borel and Serre. Zbl 0656.53049Chen, Bang-Yen; Nagano, Tadashi 35 1988 Totally geodesic submanifolds of symmetric spaces. I. Zbl 0368.53038Chen, Bang-Yen; Nagano, Tadashi 33 1977 Warped product pointwise bi-slant submanifolds of Kaehler manifolds. Zbl 1413.53101Chen, Bang-Yen; Uddin, Siraj 33 2018 Total mean curvature and submanifolds of finite type. 2nd ed. Zbl 1326.53004Chen, Bang-Yen 32 2015 Some results on concircular vector fields and their applications to Ricci solitons. Zbl 1343.53038Chen, Bang-Yen 32 2015 An exotic totally real minimal immersion of \(S^ 3\) in \(\mathbb{C} P^ 3\) and its characterisation. Zbl 0855.53011Chen, B.-Y.; Dillen, F.; Verstraelen, L.; Vrancken, L. 31 1996 Complex extensors and Lagrangian submanifolds in complex Euclidean spaces. Zbl 0877.53041Chen, Bang-Yen 30 1997 Totally real submanifolds of \(\mathbb{C} P^ n\) satisfying a basic equality. Zbl 0816.53034Chen, B.-Y.; Dillen, F.; Verstraelen, L.; Vrancken, L. 28 1994 Interaction of Legendre curves and Lagrangian submanifolds. Zbl 0884.53014Chen, Bang-Yen 28 1997 Surfaces of revolution with pointwise 1-type Gauss map. Zbl 1082.53004Chen, Bang-Yen; Choi, Miekyung; Kim, Young Ho 26 2005 Yamabe and quasi-Yamabe solitons on Euclidean submanifolds. Zbl 1425.53050Chen, Bang-Yen; Deshmukh, Sharief 25 2018 Two theorems on Kähler manifolds. Zbl 0295.53028Chen, Bang-yen; Ogiue, Koichi 25 1974 Minimal submanifolds of a higher dimensional sphere. Zbl 0218.53073Yano, Kentaro; Chen, Bang-Yen 25 1971 On the concurrent vector fields of immersed manifolds. Zbl 0221.53049Yano, Kentaro; Chen, Bang-Yen 25 1971 Null 2-type surfaces in \(E^ 3\) are circular cylinders. Zbl 0657.53002Chen, Bang-Yen 24 1988 A general inequality for submanifolds in complex-space-forms and its applications. Zbl 0871.53043Chen, Bang-yen 24 1996 Ricci solitons and concurrent vector fields. Zbl 1334.53032Chen, Bang-Yen; Deshmukh, Sharief 23 2015 Classification of marginally trapped Lorentzian flat surfaces in \(\mathbb E^4_2\) and its application to biharmonic surfaces. Zbl 1160.53007Chen, Bang-Yen 23 2008 Another general inequality for CR-warped products in complex space forms. Zbl 1049.53039Chen, Bang-Yen 23 2003 On rectifying curves in Euclidean 3-space. Zbl 1424.53021Deshmukh, Sharief; Chen, Bang-Yen; Alshammari, Sana Hamoud 23 2018 On the total curvature of immersed manifolds. I: An inequality of Fenchel-Borsuk-Willmore. Zbl 0209.52803Chen, B.-y. 23 1971 Curvature inequalities for Lagrangian submanifolds: the final solution. Zbl 1288.53014Chen, Bang-Yen; Dillen, Franki; Van der Veken, Joeri; Vrancken, Luc 23 2013 A note on Yamabe solitons. Zbl 1408.53051Deshmukh, S.; Chen, B. Y. 22 2018 Differential geometry of real submanifolds in a Kaehler manifold. Zbl 0451.53041Chen, Bang-Yen 22 1981 Marginally trapped surfaces in Lorentzian space forms with positive relative nullity. Zbl 1141.53065Chen, Bang-Yen; Van der Veken, Joeri 22 2007 Complete classification of parallel surfaces in 4-dimensional Lorentzian space forms. Zbl 1182.53018Chen, Bang-Yen; Van der Veken, Joeri 22 2009 Riemannian submanifolds. Zbl 0968.53002Chen, Bang-Yen 21 2000 Ruled surfaces and tubes with finite type Gauss map. Zbl 0798.53055Baikoussis, Christos; Chen, Bang-yen; Verstraelen, Leopold 21 1993 Quaternion CR-submanifolds of quaternion manifolds. Zbl 0481.53046Barros, M.; Chen, B. Y.; Urbano, F. 21 1981 CR-submanifolds of a Kähler manifold. II. Zbl 0485.53051Chen, Bang-Yen 21 1981 Geometry of warped products as Riemannian submanifolds and related problems. Zbl 1012.53051Chen, Bang-Yen 21 2002 Some characterizations of complex space forms in terms of Chern classes. Zbl 0315.53034Chen, Bang-Yen; Ogiue, Koichi 21 1975 Lagrangian isometric immersions of a real-space-form \(M^n(c)\) into a complex-space-form \(\widetilde M^n(4c)\). Zbl 0929.53008Chen, B.-Y.; Dillen, F.; Verstraelen, L.; Vrancken, L. 20 1998 CR-warped products in complex projective spaces with compact holomorphic factor. Zbl 1063.53056Chen, Bang-Yen 20 2004 Some open problems and conjectures on submanifolds of finite type: recent development. Zbl 1287.53044Chen, Bang-Yen 20 2014 Surfaces with parallel normalized mean curvature vector. Zbl 0435.53040Chen, Bang-Yen 20 1980 Finite type submanifolds in pseudo-Euclidean spaces and applications. Zbl 0586.53022Chen, Bang-Yen 19 1985 Special conformally flat spaces and canal hypersurfaces. Zbl 0266.53043Chen, Bang-yen; Yano, Kentaro 19 1973 A Riemannian invariant and its applications to submanifold theory. Zbl 0834.53045Chen, Bang-Yen 19 1995 Integral formulas for submanifolds and their applications. Zbl 0203.53802Chen, B.-y.; Yano, K. 19 1971 Optimal general inequalities for Lagrangian submanifolds in complex space forms. Zbl 1217.53082Chen, Bang-Yen; Dillen, Franki 18 2011 Stationary 2-type surfaces in a hypersphere. Zbl 0613.53023Barros, Manuel; Chen, Bang-Yen 18 1987 Isometric, holomorphic and symplectic reflections. Zbl 0673.53035Chen, B. Y.; Vanhecke, L. 18 1989 Differential geometry of submanifolds with planar normal sections. Zbl 0486.53004Chen, Bang-Yen 18 1982 Some topological obstructions to Bochner-Kähler metric and their applications. Zbl 0354.53049Chen, Bang-yen 18 1978 Surfaces of finite type in Euclidean 3-space. Zbl 0628.53011Chen, Bang-Yen 17 1987 Ruled surface of finite type. Zbl 0704.53003Chen, Bang-Yen; Dillen, Franki; Verstraelen, Leopold; Vrancken, Luc 17 1990 Classification of Wintgen ideal surfaces in Euclidean 4-space with equal Gauss and normal curvatures. Zbl 1203.53005Chen, Bang-Yen 17 2010 Riemannian submersions, \(\delta\)-invariants, and optimal inequality. Zbl 1253.53057Alegre, Pablo; Chen, Bang-Yen; Munteanu, Marian Ioan 17 2012 Biharmonic submanifolds and biharmonic maps in Riemannian geometry. Zbl 1455.53002Ou, Ye-Lin; Chen, Bang-Yen 17 2020 Scalar curvature, inequality and submanifold. Zbl 0256.53041Chen, Bang-Yen; Okumura, Masafumi 16 1973 Ideal Lagrangian immersions in complex space forms. Zbl 0980.53096Chen, Bang-Yen 16 2000 On spectral decomposition of immersions of finite type. Zbl 0771.53033Chen, Bang-Yen; Petrovic, Mira 16 1991 Solutions to homogeneous Monge-Ampère equations of homothetic functions and their applications to production models in economics. Zbl 1442.35464Chen, Bang-Yen 16 2014 On the surface with parallel mean curvature vector. Zbl 0252.53021Chen, Bang-Yen 16 1973 Finite type submanifolds and generalizations. Zbl 0586.53023Chen, Bang-yen 15 1985 Totally umbilical submanifolds. Zbl 0442.53051Chen, Bang-Yen 15 1980 Strings of Riemannian invariants, inequalities, ideal immersions and their applications. Zbl 1009.53041Chen, Bang-Yen 15 1998 Submanifolds with geodesic normal sections. Zbl 0536.53053Chen, Bang-Yen; Verheyen, Paul 15 1984 Slant submanifolds in complex Euclidean spaces. Zbl 0735.53040Chen, Bang-Yen; Tazawa, Yoshihiko 15 1991 Harmonic metrics, harmonic tensors, and Gauss maps. Zbl 0543.58015Chen, Bang-yen; Nagano, Tadashi 15 1984 Jacobi’s elliptic functions and Lagrangian immersions. Zbl 0866.53045Chen, Bang-Yen 14 1996 Slant submanifolds of complex projective and complex hyperbolic spaces. Zbl 0979.53058Chen, Bang-Yen; Tazawa, Yoshihiko 14 2000 Submanifolds with planar normal sections. Zbl 0485.53004Chen, Bang-Yen 14 1981 Differential geometry of rectifying submanifolds. Zbl 1375.53008Chen, Bang-Yen 14 2016 The canonical foliations of a locally conformal Kähler manifold. Zbl 0587.53059Chen, Bang-Yen; Piccinni, Paolo 13 1985 Lagrangian submanifolds in complex space forms satisfying equality in the optimal inequality involving \(\delta (2, \ldots, 2)\). Zbl 1475.53023Chen, Bang-Yen; Vrancken, Luc; Wang, Xianfeng 3 2021 Geometry of pointwise semi-slant warped products in locally conformal Kähler manifolds. (Geometry of pointwise semi-slant warped products in locally conformal Kaehler manifolds.) Zbl 1485.53030Alghamdi, Fatimah; Chen, Bang-Yen; Uddin, Siraj 1 2021 Biharmonic submanifolds and biharmonic maps in Riemannian geometry. Zbl 1455.53002Ou, Ye-Lin; Chen, Bang-Yen 17 2020 A generalized Wintgen inequality for quaternionic CR-submanifolds. Zbl 1439.53054Alodan, Haila; Chen, Bang-Yen; Deshmukh, Sharief; Vîlcu, Gabriel-Eduard 4 2020 Geometry of pointwise CR-slant warped products in Kaehler manifolds. Zbl 1468.53011Chen, Bang-Yen; Uddin, Siraj; Al-Solamy, Falleh R. 3 2020 Bi-warped product submanifolds of nearly Kaehler manifolds. Zbl 1434.53020Uddin, Siraj; Chen, Bang-Yen; Al-Jedani, Awatif; Alghanemi, Azeb 2 2020 A Chen first inequality for statistical submanifolds in Hessian manifolds of constant Hessian curvature. Zbl 1430.53061Chen, Bang-Yen; Mihai, Adela; Mihai, Ion 10 2019 Riemannian submanifolds with concircular canonical field. Zbl 1433.53084Chen, Bang-Yen; Wei, Shihshu Walter 5 2019 Sharp growth estimates for warping functions in multiply warped product manifolds. Zbl 1427.53046Chen, Bang-Yen; Wei, Shihshu Walter 5 2019 On some geometric properties of quasi-product production models. Zbl 1498.91217Alodan, Haila; Chen, Bang-Yen; Deshmukh, Sharief; Vîlcu, Gabriel-Eduard 3 2019 A polymorphic element formulation towards multiscale modelling of composite structures. Zbl 1440.74411Kocaman, E. S.; Chen, B. Y.; Pinho, S. T. 1 2019 Warped product pointwise bi-slant submanifolds of Kaehler manifolds. Zbl 1413.53101Chen, Bang-Yen; Uddin, Siraj 33 2018 Yamabe and quasi-Yamabe solitons on Euclidean submanifolds. Zbl 1425.53050Chen, Bang-Yen; Deshmukh, Sharief 25 2018 On rectifying curves in Euclidean 3-space. Zbl 1424.53021Deshmukh, Sharief; Chen, Bang-Yen; Alshammari, Sana Hamoud 23 2018 A note on Yamabe solitons. Zbl 1408.53051Deshmukh, S.; Chen, B. Y. 22 2018 Two-numbers and their applications – a survey. Zbl 1411.53033Chen, Bang-Yen 8 2018 Euclidean submanifolds with conformal canonical vector field. Zbl 1420.53012Chen, Bang-Yen; Deshmukh, Sharief 5 2018 Natural mates of Frenet curves in Euclidean 3-space. Zbl 1424.53020Deshmukh, Sharief; Chen, Bang-Yen; Alghanemi, Azeb 5 2018 Classification of \(\delta(2,n-2)\)-ideal Lagrangian submanifolds in \(n\)-dimensional complex space forms. Zbl 1381.53154Chen, Bang-Yen; Dillen, Franki; Van der Veken, Joeri; Vrancken, Luc 5 2018 A differential equation for Frenet curves in Euclidean 3-space and its applications. Zbl 1424.53022Deshmukh, Sharief; Chen, Bang-Yen; Turki, Nasser Bin 3 2018 A link between harmonicity of 2-distance functions and incompressibility of canonical vector fields. Zbl 1410.53059Chen, Bang-Yen 2 2018 Erratum to: “Two optimal inequalities for anti-holomorphic submanifolds and their applications”. Zbl 1407.53055Al-Solamy, Falleh R.; Chen, Bang-Yen; Deshmukh, Sharief 1 2018 Differential geometry of warped product manifolds and submanifolds. Zbl 1390.53001Chen, Bang-Yen 57 2017 Warped product bi-slant immersions in Kaehler manifolds. Zbl 1369.53039Uddin, Siraj; Chen, Bang-Yen; Al-Solamy, Falleh R. 56 2017 Topics in differential geometry associated with position vector fields on Euclidean submanifolds. Zbl 1362.53005Chen, Bang-Yen 11 2017 Rectifying curves and geodesics on a cone in the Euclidean 3-space. Zbl 1371.53002Chen, Bang-Yen 11 2017 Classification of torqued vector fields and its applications to Ricci solitons. Zbl 1488.53152Chen, Bang-Yen 8 2017 Addendum to: “Differential geometry of rectifying submanifolds”. Zbl 1473.53010Chen, Bang-Yen 7 2017 Rectifying submanifolds of Riemannian manifolds and torqued vector fields. Zbl 1488.53178Chen, Bang-Yen 6 2017 A link between torse-forming vector fields and rotational hypersurfaces. Zbl 1380.53012Chen, Bang-Yen; Verstraelen, Leopold 5 2017 Euclidean submanifolds via tangential components of their position vector fields. Zbl 1391.37044Chen, Bang-Yen 4 2017 Covering maps and ideal embeddings of compact homogeneous spaces. Zbl 1391.53063Chen, Bang-Yen 2 2017 Classification of rectifying space-like submanifolds in pseudo-Euclidean spaces. Zbl 1442.53008Chen, Bang-Yen; Oh, Yun Myung 2 2017 Euclidean submanifolds with incompressible canonical vector field. Zbl 1488.53010Chen, Bang-Yen 2 2017 Borsuk-Ulam theorem and maximal antipodal sets of compact symmetric spaces. Zbl 1379.55001Chen, Bang-Yen 1 2017 Differential geometry of concircular submanifolds of Euclidean spaces. Zbl 1488.53011Chen, Bang-Yen; Wei, Shihshu Walter 1 2017 Differential geometry of rectifying submanifolds. Zbl 1375.53008Chen, Bang-Yen 14 2016 A survey on Ricci solitons on Riemannian submanifolds. Zbl 1360.53048Chen, Bang-Yen 7 2016 Concircular vector fields and pseudo-Kähler manifolds. (Concircular vector fields and pseudo-Kaehler manifolds.) Zbl 1474.53280Chen, Bang-Yen 4 2016 CR-warped submanifolds in Kaehler manifolds. Zbl 1351.32064Chen, Bang-Yen 2 2016 CR-submanifolds and \(\delta \)-invariants. Zbl 1351.32065Chen, Bang-Yen 1 2016 Total mean curvature and submanifolds of finite type. 2nd ed. Zbl 1326.53004Chen, Bang-Yen 32 2015 Some results on concircular vector fields and their applications to Ricci solitons. Zbl 1343.53038Chen, Bang-Yen 32 2015 Ricci solitons and concurrent vector fields. Zbl 1334.53032Chen, Bang-Yen; Deshmukh, Sharief 23 2015 \(\delta(3)\)-ideal null 2-type hypersurfaces in Euclidean spaces. Zbl 1327.53008Chen, Bang-Yen; Fu, Yu 8 2015 Classification of ideal submanifolds of real space forms with type number \(\leq 2\). Zbl 1326.53078Chen, Bang-Yen; Yıldırım, Handan 5 2015 Geometric and topological obstructions to various immersions in submanifold theory and some related open problems. Zbl 1474.53265Chen, Bang-Yen 2 2015 Einstein manifolds as affine hypersurfaces. Zbl 1315.53042Chen, Bang-Yen 1 2015 A simple characterization of generalized Robertson-Walker spacetimes. Zbl 1308.83159Chen, Bang-Yen 43 2014 Some open problems and conjectures on submanifolds of finite type: recent development. Zbl 1287.53044Chen, Bang-Yen 20 2014 Solutions to homogeneous Monge-Ampère equations of homothetic functions and their applications to production models in economics. Zbl 1442.35464Chen, Bang-Yen 16 2014 Geometry of compact shrinking Ricci solitons. Zbl 1316.53052Chen, Bang-Yen; Deshmukh, Sharief 13 2014 Classification of Ricci solitons on Euclidean hypersurfaces. Zbl 1310.53041Chen, Bang-Yen; Deshmukh, Sharief 12 2014 Two optimal inequalities for anti-holomorphic submanifolds and their applications. Zbl 1357.53055Al-Solamy, Falleh R.; Chen, Bang-Yen; Deshmukh, Sharief 11 2014 Notes on isotropic geometry of production models. Zbl 1461.91165Chen, Bang-Yen; Decu, Simona; Verstraelen, Leopold 8 2014 Ricci solitons on Riemannian submanifolds. Zbl 1333.53054Chen, Bang-Yen 3 2014 Geometry of warped product submanifolds: a survey. Zbl 1301.53049Chen, Bang-Yen 58 2013 Biharmonic ideal hypersurfaces in Euclidean spaces. Zbl 1260.53017Chen, Bang-Yen; Munteanu, Marian Ioan 38 2013 Curvature inequalities for Lagrangian submanifolds: the final solution. Zbl 1288.53014Chen, Bang-Yen; Dillen, Franki; Van der Veken, Joeri; Vrancken, Luc 23 2013 Recent developments of biharmonic conjecture and modified biharmonic conjectures. Zbl 1300.53013Chen, Bang-Yen 10 2013 A tour through \(\delta\)-invariants: from Nash’s embedding theorem to ideal immersions, best ways of living and beyond. Zbl 1340.53001Chen, Bang-Yen 10 2013 Geometric classifications of homogeneous production functions. Zbl 1334.91043Chen, Bang-Yen; Vîlcu, Gabriel Eduard 10 2013 On ideal hypersurfaces of Euclidean 4-space. Zbl 1280.53052Chen, Bang-Yen 4 2013 Optimal inequalities, contact \(\delta\)-invariants and their applications. Zbl 1279.53048Chen, Bang-Yen; Martin-Molina, Veronica 3 2013 The 2-ranks of connected compact Lie groups. Zbl 1294.22006Chen, Bang-Yen 3 2013 Lagrangian submanifolds with prescribed second fundamental form. Zbl 1303.53096Chen, Bang-Yen; Van der Veken, Joeri; Vrancken, Luc 2 2013 Classification of spherical Lagrangian submanifolds in complex Euclidean spaces. Zbl 1308.53120Chen, Bang-Yen 2 2013 Geometry of position function of totally real submanifolds in complex Euclidean spaces. Zbl 1473.53078Chen, Bang-Yen 2 2013 Pointwise slant submanifolds in almost Hermitian manifolds. Zbl 1269.53059Chen, Bang-Yen; Garay, Oscar J. 46 2012 Riemannian submersions, \(\delta\)-invariants, and optimal inequality. Zbl 1253.53057Alegre, Pablo; Chen, Bang-Yen; Munteanu, Marian Ioan 17 2012 On some geometric properties of quasi-sum production models. Zbl 1243.39019Chen, Bang-Yen 12 2012 \(\delta (2)\)-ideal null 2-type hypersurfaces of Euclidean space are spherical cylinders. Zbl 1247.53067Chen, Bang-Yen; Garay, Oscar J. 10 2012 An optimal inequality for CR-warped products in complex space forms involving CR \(\delta \)-invariant. Zbl 1244.53059Chen, Bang-Yen 9 2012 Classification of \(h\)-homogeneous production functions with constant elasticity of substitution. Zbl 1260.91161Chen, Bang-Yen 8 2012 Lagrangian submanifolds in complex space forms attaining equality in a basic inequality. Zbl 1246.53108Chen, Bang-Yen; Dillen, Franki; Vrancken, Luc 7 2012 A note on homogeneous production models. Zbl 1299.91088Chen, Bang-Yen 7 2012 Classification of homothetic functions with constant elasticity of substitution and its geometric applications. Zbl 1308.90060Chen, Bang-Yen 7 2012 Geometry of quasi-sum production functions with constant elasticity of substitution property. Zbl 1273.90072Chen, Bang-Yen 6 2012 Classification of Lagrangian submanifolds in complex space forms satisfying a basic equality involving \(\delta(2,2)\). Zbl 1237.53045Chen, Bang-Yen; Prieto-Martín, Alicia 5 2012 Geometry of \(\mathcal P R\)-warped products in para-Kähler manifolds. Zbl 1260.53039Chen, Bang-Yen; Munteanu, Marian Ioan 5 2012 An explicit formula of Hessian determinants of composite functions and its applications. Zbl 1289.15015Chen, Bang-Yen 2 2012 Wintgen ideal surfaces in four-dimensional neutral indefinite space form \({R^4_2(c)}\). Zbl 1267.53054Chen, Bang-Yen 1 2012 Pseudo-Riemannian geometry, \(\delta\)-invariants and applications. Zbl 1245.53001Chen, Bang-Yen 86 2011 Optimal general inequalities for Lagrangian submanifolds in complex space forms. Zbl 1217.53082Chen, Bang-Yen; Dillen, Franki 18 2011 Classification of minimal Lorentz surfaces in indefinite space forms with arbitrary codimension and arbitrary index. Zbl 1274.53078Chen, B.-Y. 13 2011 On some geometric properties of \(h\)-homogeneous production functions in microeconomics. Zbl 1289.91107Chen, Bang-Yen 8 2011 On Wintgen ideal surfaces. Zbl 1266.53007Chen, Bang-Yen 5 2011 \(\delta\)-invariants for Lagrangian submanifolds of complex space forms. Zbl 1264.53057Chen, Bang-Yen; Dillen, Franki 4 2011 Classification theorems for space-like surfaces in 4-dimensional indefinite space forms with index 2. Zbl 1230.53050Chen, Bang-Yen; Suceavǎ, Bogdan D. 2 2011 Lagrangian \(H\)-umbilical submanifolds of para-Kähler manifolds. Zbl 1247.53066Chen, Bang-Yen 1 2011 Classification of Wintgen ideal surfaces in Euclidean 4-space with equal Gauss and normal curvatures. Zbl 1203.53005Chen, Bang-Yen 17 2010 Classification of marginally trapped surfaces with parallel mean curvature vector in Lorentzian space forms. Zbl 1213.53026Chen, Bang-Yen; Van der Veken, Joeri 12 2010 On slant submanifolds of neutral Kähler manifolds. Zbl 1202.53022Arslan, K.; Carriazo, A.; Chen, B.-Y.; Murathan, C. 10 2010 Submanifolds with parallel mean curvature vector in Riemannian and indefinite space forms. Zbl 1214.53014Chen, Bang-Yen 7 2010 Complete classification of parallel spatial surfaces in pseudo-Riemannian space forms with arbitrary index and dimension. Zbl 1205.53061Chen, Bang-Yen 7 2010 Addendum to “classification of marginally trapped Lorentzian flat surfaces in \(\mathbb E_2^4\) and its application to biharmonic surfaces”. Zbl 1179.53021Chen, Bang-Yen; Yang, Dan 5 2010 Complete classification of Lorentz surfaces with parallel mean curvature vector in arbitrary pseudo-Euclidean space. Zbl 1207.53067Chen, Bang-Yen 4 2010 Complete classification of parallel Lorentzian surfaces in Lorentzian complex space forms. Zbl 1192.53016Chen, Bang-Yen; Dillen, Franki; Van der Veken, Joeri 4 2010 A minimal immersion of the hyperbolic plane into the neutral pseudo-hyperbolic 4-space and its characterization. Zbl 1188.53009Chen, Bang-Yen 3 2010 Explicit classification of parallel Lorentz surfaces in 4D indefinite space forms with index 3. Zbl 1217.53061Chen, Bang-Yen 2 2010 ...and 337 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,432 Authors 179 Chen, Bang-Yen 51 Siraj-Uddin 47 Vrancken, Luc 38 Vanhecke, Lieven 36 De, Uday Chand 36 Kim, Youngho 32 Vîlcu, Gabriel Eduard 30 Ali, Akram 30 Dillen, Franki 29 Verstraelen, Leopold C. A. 26 Fu, Yu 26 Oniciuc, Cezar 24 Ṣahin, Bayram 23 Al-Solamy, Falleh Rijaullah 23 Alkhaldi, Ali H. 23 Deshmukh, Sharief 22 Lee, Jaewon 21 Khan, Meraj Ali 21 Mihai, Ion 20 Garay, Oscar Jesus 20 Shahid, Mohammed Hasan 19 Hui, Shyamal Kumar 19 Mantica, Carlo Alberto 18 Barros, Manuel 18 Mihai, Adela 18 Montaldo, Stefano 18 Ou, Ye-Lin 17 Van der Veken, Joeri 16 Arslan, Kadri 16 Kumar, Rakesh 16 Urakawa, Hajime 15 Chaubey, Sudhakar Kumar 15 Hu, Zejun 15 Molinari, Luca Guido 15 Ozgur, Cihan 15 Rosca, Radu M. 15 Suh, Young Jin 15 Turgay, Nurettin Cenk 14 Fetcu, Dorel 14 Gupta, Ram Shankar 14 Lucas, Pascual 14 Sasahara, Toru 14 Yoon, Dae Won 13 Carriazo, Alfonso 13 Kılıç, Erol 13 Kim, Dongsoo S. 13 Tanaka, Makiko Sumi 13 Tasaki, Hiroyuki 13 Yano, Kentaro 12 de Lima, Henrique F. 12 Li, Haizhong 12 Milousheva, Velichka 12 Öztürk, Günay 12 Shaikh, Absos Ali 12 Shenawy, Sameh 12 Siddiqui, Aliya Naaz 11 Adachi, Toshiaki 11 Blaga, Adara-Monica 11 Blair, David E. 11 Bulca, Betül 11 Dragomir, Sorin 11 Houh, Chorng-Shi 11 Maeta, Shun 11 Mohammadpouri, Akram 11 Murathan, Cengizhan 11 Nagaich, Rakesh Kumar 11 Othman, Wan Ainun Mior 11 Park, Kwang-Soon 11 Tripathi, Mukut Mani 10 Akyol, Mehmet Akif 10 Atçeken, Mehmet 10 Castro, Ildefonso 10 İlarslan, Kazim 10 Khan, Viqar Azam 10 Kumar, Sangeet 10 Lone, Mehraj Ahmad 10 Lone, Mohamd Saleem 10 Pal, Tanumoy 10 Pashaie, Firooz 10 Prasad, Rajendra 10 Yang, Dan 9 Antic, Miroslava 9 Deszcz, Ryszard 9 Dursun, Uǧur 9 Hasanis, Thomas 9 Maeda, Sadahiro 9 Mofarreh, Fatemah Y. Y. 9 Munteanu, Marian-Ioan 9 Perktas, Selcen Yuksel 9 Ratto, Andrea 9 Sharma, Ramesh 9 Suceavă, Bogdan Dragos 9 Taştan, Hakan Mete 9 Vlachos, Theodoros 9 Wang, Xianfeng 8 Berndt, Jürgen 8 Bhattacharyya, Arindam 8 Choudhary, Majid Ali 8 Crâşmăreanu, Mircea 8 Djorić, Mirjana ...and 1,332 more Authors all top 5 Cited in 270 Serials 107 Journal of Geometry and Physics 75 Journal of Geometry 62 Differential Geometry and its Applications 60 Filomat 58 Kodai Mathematical Journal 54 Results in Mathematics 54 Mediterranean Journal of Mathematics 50 Journal of Mathematical Analysis and Applications 45 Proceedings of the American Mathematical Society 40 Tôhoku Mathematical Journal. Second Series 40 Annals of Global Analysis and Geometry 36 Geometriae Dedicata 36 International Journal of Geometric Methods in Modern Physics 35 Annali di Matematica Pura ed Applicata. Serie Quarta 31 The Journal of Geometric Analysis 31 International Electronic Journal of Geometry 28 Bulletin of the Australian Mathematical Society 28 Archiv der Mathematik 26 Israel Journal of Mathematics 24 Transactions of the American Mathematical Society 24 Turkish Journal of Mathematics 23 Mathematische Zeitschrift 23 Kodai Mathematical Seminar Reports 21 Czechoslovak Mathematical Journal 19 Mathematische Annalen 19 International Journal of Mathematics 18 Rocky Mountain Journal of Mathematics 18 Glasgow Mathematical Journal 18 Communications of the Korean Mathematical Society 16 Monatshefte für Mathematik 16 Journal of Inequalities and Applications 15 Journal of Mathematical Physics 15 Rendiconti del Circolo Matemàtico di Palermo. Serie II 15 DGDS. Differential Geometry – Dynamical Systems 15 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 15 AIMS Mathematics 14 Acta Mathematica Sinica. English Series 13 Manuscripta Mathematica 13 Tokyo Journal of Mathematics 13 Balkan Journal of Geometry and its Applications (BJGA) 13 Hacettepe Journal of Mathematics and Statistics 13 Advances in Mathematical Physics 13 Afrika Matematika 12 General Relativity and Gravitation 12 Advances in Mathematics 12 Facta Universitatis. Series Mathematics and Informatics 12 Taiwanese Journal of Mathematics 11 Acta Mathematica Hungarica 11 Calculus of Variations and Partial Differential Equations 11 Abstract and Applied Analysis 11 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 11 Palestine Journal of Mathematics 10 Journal of Soviet Mathematics 10 Kyungpook Mathematical Journal 10 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 10 Journal of Mathematical Sciences (New York) 10 Communications de la Faculté des Sciences de l’Université d’Ankara. Séries A1. Mathematics and Statistics 10 Asian-European Journal of Mathematics 9 Indian Journal of Pure & Applied Mathematics 9 Mathematical Notes 9 Advances in Geometry 9 Science China. Mathematics 8 Ukrainian Mathematical Journal 8 International Journal of Mathematics and Mathematical Sciences 8 Journal of the Mathematical Society of Japan 8 Osaka Journal of Mathematics 8 Proceedings of the Japan Academy. Series A 8 Arab Journal of Mathematical Sciences 8 Honam Mathematical Journal 8 Proceedings of the National Academy of Sciences, India. Section A. Physical Sciences 8 Journal of Dynamical Systems and Geometric Theories 8 Bulletin of the American Mathematical Society 7 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 7 Applied Mathematics and Computation 7 Mathematische Nachrichten 7 Nagoya Mathematical Journal 7 Quaestiones Mathematicae 7 Annales de la Faculté des Sciences de Toulouse. Série V. Mathématiques 7 Kragujevac Journal of Mathematics 7 Boletim da Sociedade Paranaense de Matemática. Terceira Série 7 ISRN Geometry 6 Beiträge zur Algebra und Geometrie 6 Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 6 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section A. Physique Théorique 6 Mathematica Slovaca 6 Tamkang Journal of Mathematics 6 Note di Matematica 6 Bulletin of the Iranian Mathematical Society 6 Lobachevskii Journal of Mathematics 6 Central European Journal of Mathematics 6 Cubo 6 Frontiers of Mathematics in China 6 Acta Universitatis Sapientiae. Mathematica 6 Mathematics 5 Periodica Mathematica Hungarica 5 Chaos, Solitons and Fractals 5 Journal of the Korean Mathematical Society 5 Pacific Journal of Mathematics 5 Rendiconti del Seminario Matematico della Università di Padova 5 Linear Algebra and its Applications ...and 170 more Serials all top 5 Cited in 45 Fields 2,078 Differential geometry (53-XX) 197 Global analysis, analysis on manifolds (58-XX) 80 Several complex variables and analytic spaces (32-XX) 64 Relativity and gravitational theory (83-XX) 51 Partial differential equations (35-XX) 41 Manifolds and cell complexes (57-XX) 38 Calculus of variations and optimal control; optimization (49-XX) 20 Algebraic geometry (14-XX) 16 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 15 Nonassociative rings and algebras (17-XX) 15 Topological groups, Lie groups (22-XX) 13 Dynamical systems and ergodic theory (37-XX) 11 Convex and discrete geometry (52-XX) 10 Potential theory (31-XX) 10 Geometry (51-XX) 10 Quantum theory (81-XX) 9 Functions of a complex variable (30-XX) 9 Algebraic topology (55-XX) 8 Linear and multilinear algebra; matrix theory (15-XX) 7 Fluid mechanics (76-XX) 6 Ordinary differential equations (34-XX) 6 Operations research, mathematical programming (90-XX) 5 Statistics (62-XX) 4 Real functions (26-XX) 3 History and biography (01-XX) 3 Number theory (11-XX) 3 Functional analysis (46-XX) 3 Probability theory and stochastic processes (60-XX) 3 Numerical analysis (65-XX) 3 Computer science (68-XX) 3 Mechanics of particles and systems (70-XX) 2 Mathematical logic and foundations (03-XX) 2 Combinatorics (05-XX) 2 Group theory and generalizations (20-XX) 2 Measure and integration (28-XX) 2 Mechanics of deformable solids (74-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Astronomy and astrophysics (85-XX) 2 Information and communication theory, circuits (94-XX) 1 General and overarching topics; collections (00-XX) 1 Associative rings and algebras (16-XX) 1 Difference and functional equations (39-XX) 1 Operator theory (47-XX) 1 General topology (54-XX) 1 Classical thermodynamics, heat transfer (80-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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