Edit Profile (opens in new tab) García-Río, Eduardo Compute Distance To: Compute Author ID: garcia-rio.eduardo Published as: García-Río, Eduardo; García-Río, E.; García-Rio, Eduardo; García Río, Eduardo; Garcìa-Rìo, Eduardo more...less External Links: ORCID Documents Indexed: 157 Publications since 1988, including 9 Books 4 Contributions as Editor Reviewing Activity: 31 Reviews Co-Authors: 50 Co-Authors with 159 Joint Publications 699 Co-Co-Authors all top 5 Co-Authors 2 single-authored 61 Vázquez-Lorenzo, Ramón 36 Brozos-Vázquez, Miguel 29 Gilkey, Peter B. 25 Calviño-Louzao, Esteban 23 Vázquez Abal, María Elena 22 Kupeli, Demir N. 15 Fernández-López, Manuel 13 Hervella, Luis M. 12 Díaz-Ramos, José Carlos 12 Matsushita, Yasuo 12 Vanhecke, Lieven 10 Bonome, Agustín 10 Castro Bolano, Regina 7 Gutiérrez-Rodríguez, Ixchel 6 Valle-Regueiro, Xabier 5 Gavino Fernández, Sandra 5 Haji-Badali, Ali 5 Nikčević, Stana Ž. 4 Caeiro-Oliveira, Sandro 3 Mariño-Villar, Rodrigo 3 Park, Jeonghyeong 3 Seoane-Bascoy, Javier 3 Ünal, Bülent 2 Calvaruso, Giovanni 2 Davidov, Johann T. 2 Erkekoğlu, Fazilet 2 Ferreiro-Subrido, M. 2 Fiedler, Bernd 1 Álvarez López, Jesús Antonio 1 Batat, Wafaa 1 Boucherif, Abdelkader 1 Castro, Paula Maria 1 Cendán-Verdes, J. 1 Cordero, Luis A. 1 Cortés Ayaso, Alexandre Andrés 1 Garay, Oscar Jesus 1 García-Martínez, Xabier 1 García-Ramírez, Iago 1 Hashimoto, Hideya 1 Haze, Seiya 1 Hervella, Luis Maria 1 Katayama, Noriaki 1 Koda, Takashi 1 Nieto Roig, Juan Jose 1 Oguro, Takashi 1 Raki, Zoran 1 Sixto Neira, Marta 1 Stanilov, Grozio 1 Tsankov, Yulian Ts. 1 Videv, Veselin T. all top 5 Serials 8 Classical and Quantum Gravity 7 Journal of Geometry and Physics 6 Annals of Global Analysis and Geometry 5 Proceedings of the American Mathematical Society 5 Synthesis Lectures on Mathematics and Statistics 4 Annali di Matematica Pura ed Applicata. Serie Quarta 4 Results in Mathematics 4 Differential Geometry and its Applications 3 General Relativity and Gravitation 3 Journal of Mathematical Physics 3 Geometriae Dedicata 3 Kodai Mathematical Journal 3 Monatshefte für Mathematik 3 Pacific Journal of Mathematics 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Advances in Geometry 3 International Journal of Geometric Methods in Modern Physics 3 Publicaciones del Departamento de Geometría y Topología, Universidad de Santiago de Compostela 2 Israel Journal of Mathematics 2 Journal of Mathematical Analysis and Applications 2 Archiv der Mathematik 2 Bulletin of the London Mathematical Society 2 Illinois Journal of Mathematics 2 Journal of Differential Equations 2 Journal of Geometry 2 Journal of the Mathematical Society of Japan 2 Manuscripta Mathematica 2 Mathematische Nachrichten 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Tsukuba Journal of Mathematics 2 International Journal of Mathematics 2 Matemática Contemporânea 2 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Houston Journal of Mathematics 1 Mathematical Methods in the Applied Sciences 1 Rocky Mountain Journal of Mathematics 1 Acta Scientiarum Mathematicarum 1 Canadian Journal of Mathematics 1 Canadian Mathematical Bulletin 1 Czechoslovak Mathematical Journal 1 Indiana University Mathematics Journal 1 Mathematische Annalen 1 Mathematische Zeitschrift 1 Osaka Journal of Mathematics 1 Publicationes Mathematicae Debrecen 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Rivista di Matematica della Università di Parma. Serie IV 1 Rendiconti di Matematica e delle sue Applicazioni. Serie VII 1 Acta Mathematica Hungarica 1 Acta Applicandae Mathematicae 1 Journal of Applied Mathematics and Stochastic Analysis 1 Mathematics Journal of Toyama University 1 The Journal of Geometric Analysis 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Journal of Physics A: Mathematical and General 1 Linear Algebra and its Applications 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Bollettino della Unione Matemàtica Italiana. Serie VII. A 1 Rivista di Matematica della Università di Parma. Serie V 1 Arab Journal of Mathematical Sciences 1 Balkan Journal of Geometry and its Applications (BJGA) 1 The Quarterly Journal of Mathematics 1 Lecture Notes in Mathematics 1 Mathematics and its Applications (Dordrecht) 1 AIP Conference Proceedings 1 Journal of Physics A: Mathematical and Theoretical 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 1 Analysis and Mathematical Physics 1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences all top 5 Fields 156 Differential geometry (53-XX) 19 Global analysis, analysis on manifolds (58-XX) 18 Relativity and gravitational theory (83-XX) 5 General and overarching topics; collections (00-XX) 3 Partial differential equations (35-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Real functions (26-XX) 2 Astronomy and astrophysics (85-XX) 1 Algebraic geometry (14-XX) 1 Topological groups, Lie groups (22-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Ordinary differential equations (34-XX) 1 Operator theory (47-XX) 1 Mechanics of deformable solids (74-XX) 1 Biology and other natural sciences (92-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 111 Publications have been cited 859 times in 501 Documents Cited by ▼ Year ▼ A remark on compact Ricci solitons. Zbl 1132.53023Fernández-López, M.; García-Río, E. 47 2008 The geometry of Walker manifolds. Zbl 1206.53039Brozos-Vázquez, Miguel; García-Río, Eduardo; Gilkey, Peter; Nikčević, Stana; Vázquez-Lorenzo, Ramón 44 2009 Three-dimensional Lorentzian homogeneous Ricci solitons. Zbl 1264.53052Brozos-Vázquez, M.; Calvaruso, G.; García-Río, E. 41 2012 Rigidity of shrinking Ricci solitons. Zbl 1226.53047Fernández-López, Manuel; García-Río, Eduardo 39 2011 Three-dimensional Lorentz manifolds admitting a parallel null vector field. Zbl 1068.53049Chaichi, M.; García-Río, E.; Vásquez-Abal, M. E. 33 2005 Locally conformally flat Lorentzian gradient Ricci solitons. Zbl 1285.53059Brozos-Vázquez, M.; García-Río, E.; Gavino-Fernández, S. 32 2013 Osserman manifolds in semi-Riemannian geometry. Zbl 1005.53040García-Río, Eduardo; Kupeli, Demir N.; Vázquez-Lorenzo, Ramón 30 2002 A curvature condition for a twisted product to be a warped product. Zbl 0999.53029Fernández-López, M.; García-Río, E.; Kupeli, D. N.; Ünal, B. 29 2001 The geometry of modified Riemannian extensions. Zbl 1186.53056Calviño-Louzao, E.; García-Río, E.; Gilkey, P.; Vázquez-Lorenzo, R. 24 2009 Ricci solitons on Lorentzian manifolds with large isometry groups. Zbl 1266.53049Batat, W.; Brozos-Vázquez, M.; García-Río, E.; Gavino-Fernández, S. 23 2011 Curvature properties of four-dimensional Walker metrics. Zbl 1086.83031Chaichi, M.; García-Río, E.; Matsushita, Y. 22 2005 Some remarks on locally conformally flat static space-times. Zbl 1076.53084Brozos-Vázquez, Miguel; García-Río, Eduardo; Vázquez-Lorenzo, Ramón 19 2005 Affine Osserman connections and their Riemann extensions. Zbl 0940.53017García-Río, Eduardo; Kupeli, Demir N.; Vázquez-Abal, M. Elena; Vázquez-Lorenzo, R. 19 1999 On a problem of Osserman in Lorentzian geometry. Zbl 0880.53017García-Río, Eduardo; Kupeli, Demir N.; Vázquez-Abal, M. Elena 17 1997 On a differential equation characterizing Euclidean spheres. Zbl 1058.53027García-Río, Eduardo; Kupeli, Demir N.; Ünal, Bülent 16 2003 On gradient Ricci solitons with constant scalar curvature. Zbl 1327.53057Fernández-López, Manuel; García-Río, Eduardo 15 2016 Semi-Riemannian maps and their applications. Zbl 0924.53003García-Río, Eduardo; Kupeli, Demir N. 14 1999 Maximum principles and gradient Ricci solitons. Zbl 1217.53042Fernández-López, Manuel; García-Río, Eduardo 13 2011 Almost Kähler Walker 4-manifolds. Zbl 1106.53046Davidov, J.; Díaz-Ramos, J. C.; García-Río, E.; Matsushita, Y.; Muškarov, O.; Vázquez-Lorenzo, R. 13 2007 Homogeneous affine surfaces: affine Killing vector fields and gradient Ricci solitons. Zbl 1394.53021Brozos-Vázquez, Miguel; García-Río, Eduardo; Gilkey, Peter B. 13 2018 Isotropic Kähler structures on Engel 4-manifolds. Zbl 0964.53047García-Río, Eduardo; Matsushita, Yasuo 12 2000 Characterizing specific Riemannian manifolds by differential equations. Zbl 1033.53033Erkekoğlu, Fazilet; García-Río, Eduardo; Kupeli, Demir N.; Ünal, Bülent 12 2003 Nonsymmetric Osserman pseudo-Riemannian manifolds. Zbl 0939.53014García-Río, Eduardo; Vázquez-Abal, M. Elena; Vázquez-Lorenzo, R. 12 1998 Singularity versus splitting theorems for stably causal spacetimes. Zbl 0861.53064García-Río, Eduardo; Kupeli, Demir N. 11 1996 Homogeneous Ricci almost solitons. Zbl 1402.53037Calviño-Louzao, Esteban; Fernández-López, Manuel; García-Río, Eduardo; Vázquez-Lorenzo, Ramón 11 2017 Homogeneity of Lorentzian three-manifolds with recurrent curvature. Zbl 1307.53057García-Río, Eduardo; Gilkey, Peter B.; Nikčević, Stana 11 2014 Paraquaternionic Kähler manifolds. Zbl 0987.53020García-Río, Eduardo; Matsushita, Yasuo; Vázquez-Lorenzo, Ramón 10 2001 Some gap theorems for gradient Ricci solitons. Zbl 1247.53051Fernández-López, Manuel; García-Río, Eduardo 10 2012 Riemann extensions of torsion-free connections with degenerate Ricci tensor. Zbl 1220.53026Calviño-Louzao, E.; García-Río, E.; Vázquez-Lorenzo, R. 10 2010 Curvature of indefinite almost contact manifolds. Zbl 1008.53032Bonome, Agustín; Castro, Regina; García-Río, Eduardo; Hervella, Luis 9 1997 Harmonic endomorphism fields. Zbl 0880.53032García-Río, Eduardo; Vanhecke, Lieven; Vázquez-Abal, M. Elena 9 1997 Hermitian-Walker 4-manifolds. Zbl 1135.53049Davidov, J.; Díaz-Ramos, J. C.; García-Río, E.; Matsushita, Y.; Muškarov, O.; Vázquez-Lorenzo, R. 9 2008 Lorentzian 3-manifolds with commuting curvature operators. Zbl 1141.53319García-Río, Eduardo; Haji-Badali, Ali; Vázquez-Abal, M. Elena; Vázquez-Lorenzo, Ramón 9 2008 Homogeneous affine surfaces: moduli spaces. Zbl 1345.53015Brozos-Vázquez, M.; García-Río, E.; Gilkey, P. 8 2016 Nonsymmetric Osserman indefinite Kähler manifolds. Zbl 0904.53022Bonome, Agustín; Castro, Regina; García-Río, Eduardo; Hervella, Luis M.; Vázquez-Lorenzo, R. 8 1998 Complete locally conformally flat manifolds of negative curvature. Zbl 1128.53018Brozos-Vázquez, Miguel; García-Río, Eduardo; Vázquez-Lorenzo, Ramón 7 2006 A note on compact Cotton solitons. Zbl 1256.83023Calviño-Louzao, E.; García-Río, E.; Vázquez-Lorenzo, R. 7 2012 Diameter bounds and Hitchin-Thorpe inequalities for compact Ricci solitons. Zbl 1198.53035Fernández-López, Manuel; García-Río, Eduardo 7 2010 On level sets of Lorentzian distance function. Zbl 1042.83006Erkekoğlu, F.; García-Río, E.; Kupeli, D. N. 7 2003 Null and infinitesimal isotropy in semi-Riemannian geometry. Zbl 0796.53018García-Río, Eduardo; Kupeli, Demir N. 6 1994 Half conformally flat generalized quasi-Einstein manifolds of metric signature \((2, 2)\). Zbl 1395.53040Brozos-Vázquez, Miguel; García-Río, Eduardo; Gilkey, Peter; Valle-Regueiro, Xabier 6 2018 New examples of Osserman metrics with nondiagonalizable Jacobi operators. Zbl 1099.53047Díaz-Ramos, J. Carlos; García-Río, Eduardo; Vázquez-Lorenzo, Ramón 6 2006 Conformally Osserman four-dimensional manifolds whose conformal Jacobi operators have complex eigenvalues. Zbl 1149.53316Brozos-Vázquez, M.; García-Río, E.; Vázquez-Lorenzo, R. 6 2006 Locally conformally flat Lorentzian quasi-Einstein manifolds. Zbl 1291.53021Brozos-Vázquez, M.; García-Río, E.; Gavino-Fernández, S. 5 2014 Four-dimensional Osserman symmetric spaces. Zbl 1008.53023García-Río, Eduardo; Vázquez-Lorenzo, Ramón 5 2001 Pseudo-Riemannian manifolds with simple Jacobi operators. Zbl 1042.53011Bonome, Agustin; Castro, Regina; García-Rio, Eduardo; Hervella, Luis; Vázquez-Lorenzo, Ramón 5 2002 Higher-dimensional Osserman metrics with non-nilpotent Jacobi operators. Zbl 1237.53070Calviño-Louzao, E.; García-Río, E.; Gilkey, P.; Vázquez-Lorenzo, R. 5 2012 Lorentzian three-manifolds with special curvature operators. Zbl 1132.83014García-Río, E.; Badali, A. Haji; Vázquez-Lorenzo, R. 5 2008 Null holomorphically flat indefinite almost Hermitian manifolds. Zbl 0874.53024Bonome, Agustín; Castro, Regina; García-Río, Eduardo; Hervella, Luis M.; Matsushita, Y. 4 1995 Half conformally flat gradient Ricci almost solitons. Zbl 1371.53024Brozos-Vázquez, M.; García-Río, E.; Valle-Regueiro, X. 4 2016 Geometric properties of generalized symmetric spaces. Zbl 1335.53067Calviño-Louzao, Esteban; García-Río, Eduardo; Vázquez-Abal, María Elena; Vázquez-Lorenzo, Ramón 4 2015 Four-dimensional neutral signature self-dual gradient Ricci solitons. Zbl 1358.53045García-Río, Eduardo; Brozos-Vázquez, Miguel 4 2016 A note on locally conformally flat gradient Ricci solitons. Zbl 1284.53046Fernández-López, Manuel; García-Río, Eduardo 4 2014 Pseudo-Chern classes and opposite Chern classes of indefinite almost Hermitian manifolds. Zbl 0923.53009Bonome, Agustín; Castro, Regina; García-Río, Eduardo; Hervella, Luis M.; Matsushita, Y. 4 1997 Warped product metrics and locally conformally flat structures. Zbl 1098.53023Brozos-Vázquez, M.; García-Río, E.; Vázquez-Lorenzo, R. 4 2005 The structure of the Ricci tensor on locally homogeneous Lorentzian gradient Ricci solitons. Zbl 1411.53036Brozos-Vázquez, M.; García-Río, E.; Gavino-Fernández, S.; Gilkey, P. 4 2018 Relating the curvature tensor and the complex Jacobi operator of an almost Hermitian manifold. Zbl 1180.53030Brozos-Vázquez, M.; García-Río, E.; Gilkey, P. 4 2008 Three-dimensional homogeneous critical metrics for quadratic curvature functionals. Zbl 1480.53053Brozos-Vázquez, M.; García-Río, E.; Caeiro-Oliveira, S. 3 2021 Almost complex manifolds with holomorphic distributions. Zbl 0813.53018Bonome, Agustín; Castro, Regina; García-Río, Eduardo; Hervella, Luis M.; Matsushita, Y. 3 1994 Bach-flat isotropic gradient Ricci solitons. Zbl 1387.53058Calviño-Louzao, Esteban; García-Río, Eduardo; Gutiérrez-Rodríguez, Ixchel; Vázquez-Lorenzo, Ramón 3 2018 Homothety curvature homogeneity and homothety homogeneity. Zbl 1343.53072García-Río, E.; Gilkey, P.; Nikčević, S. 3 2015 A note on the structure of algebraic curvature tensors. Zbl 1056.53014Díaz-Ramos, J. Carlos; García-Río, Eduardo 3 2004 Four-dimensional Osserman-Ivanov-Petrova metrics of neutral signature. Zbl 1114.83300Calviño-Louzao, Esteban; García-Río, Eduardo; Vázquez-Lorenzo, Ramón 3 2007 Four-dimensional manifolds with degenerate self-dual Weyl curvature operator. Zbl 1181.53030Cortés-Ayaso, Alexandre; Díaz-Ramos, J. Carlos; García-Río, Eduardo 3 2008 Examples of signature \((2,2)\) manifolds with commuting curvature operators. Zbl 1129.53058Brozos-Vázquez, M.; García-Río, E.; Gilkey, P.; Vázquez-Lorenzo, R. 3 2007 A natural linear equation in affine geometry: the affine quasi-Einstein equation. Zbl 1392.53056Brozos-Vázquez, Miguel; García-Río, Eduardo; Gilkey, Peter; Valle-Regueiro, Xabier 3 2018 Affine surfaces which are Kähler, para-Kähler, or nilpotent Kähler. Zbl 1400.53029Calviño-Louzao, E.; García-Río, E.; Gilkey, P.; Gutiérrez-Rodríguez, I.; Vázquez-Lorenzo, R. 3 2018 A local characterization of Schwarzschild and Reissner metrics. Zbl 0836.53013García-Río, Eduardo; Kupeli, Demir N. 2 1994 On the holomorphic sectional curvature on an indefinite Kähler manifold. Zbl 0765.53051Bonome, Agustín; Castro, Regina; García-Río, Eduardo; Hervella, Luis M. 2 1992 Curvature properties of para-Kähler manifolds. Zbl 0843.53029García-Río, Eduardo; Hervella, Luis M.; Vásquez-Lorenzo, R. 2 1996 On the semi-Riemannian structure of the tangent bundle of a two-point homogeneous space. Zbl 0851.53021Cendán-Verdes, J.; García-Río, Eduardo; Vázquez-Abal, M. Elena 2 1994 On the paraholomorphic sectional curvature of almost para-Hermitian manifolds. Zbl 0965.53052Bonome, A.; Castro, R.; García-Río, E.; Hervella, L.; Vázquez-Lorenzo, R. 2 1998 Aspects of differential geometry. III. Zbl 1371.53001Calviño-Louzao, Esteban; García-Río, Eduardo; Gilkey, Peter; Park, JeongHyeong; Vázquez-Lorenzo, Ramón 2 2017 Symplectic, Hermitian and Kähler structures on Walker 4-manifolds. Zbl 1173.53030García-Río, Eduardo; Haze, Seiya; Katayama, Noriaki; Matsushita, Yasuo 2 2008 Total curvatures of geodesic spheres associated to quadratic curvature invariants. Zbl 1098.53026García-Río, Eduardo; Díaz-Ramos, J. Carlos.; Hervella, Luis 2 2005 Geodesic transformations and space forms. Zbl 1076.53510García-Río, Eduardo; Vanhecke, Lieven 2 1997 The structure of algebraic covariant derivative curvature tensors. Zbl 1080.53017Díaz-Ramos, J.; Fiedler, B.; García-Río, E.; Gilkey, P. 2 2004 Four-dimensional Osserman metrics of neutral signature. Zbl 1186.53028García-Río, Eduardo; Gilkey, Peter B.; Vázquez-Abal, M. Elena; Vázquez-Lorenzo, Ramón 2 2010 A sharp lower bound for the scalar curvature of certain steady gradient Ricci solitons. Zbl 1277.53041Fernández-López, Manuel; García-Río, Eduardo 2 2013 Generalized Osserman four-dimensional manifolds. Zbl 1004.53049Bonome, Agustín; Castro, Paula; García-Río, Eduardo 2 2001 Conformally Einstein and Bach-flat four-dimensional homogeneous manifolds. Zbl 1423.53057Calviño-Louzao, E.; García-Martínez, Xabier; García-Río, Eduardo; Gutiérrez-Rodríguez, Ixcheldzohara; Vázquez-Lorenzo, R. 2 2019 Local structure of self-dual gradient Yamabe solitons. Zbl 1372.53070Brozos-Vázquez, Miguel; Calviño-Louzao, Esteban; García-Río, Eduardo; Vázquez-Lorenzo, Ramón 2 2016 Osserman metrics on Walker 4-manifolds equipped with a para-Hermitian structure. Zbl 1152.53311Díaz-Ramon, J. Carlos; García-Río, Eduardo; Vázquez-Lorenzo, Ramón 2 2006 Osserman and conformally Osserman manifolds with warped and twisted product structure. Zbl 1161.53025Brozos-Vázquez, Miguel; García-Río, Eduardo; Vázquez-Lorenzo, Ramón 2 2008 Curvature operators and generalizations of symmetric spaces in Lorentzian geometry. Zbl 1260.53122Calviño-Louzao, E.; García-Río, E.; Vázquez-Abal, M. E.; Vázquez-Lorenzo, R. 2 2012 Critical metrics for all quadratic curvature functionals. Zbl 1471.58016Brozos-Vázquez, Miguel; Caeiro-Oliveira, Sandro; García-Río, Eduardo 1 2021 Isotropic quasi-Einstein manifolds. Zbl 1478.83009Brozos-Vázquez, M.; García-Río, E.; Valle-Regueiro, X. 1 2019 Critical metrics and massive gravity solutions on three-dimensional Brinkmann waves. Zbl 07442583Brozos-Vázquez, M.; Caeiro-Oliveira, S.; García-Río, E. 1 2022 Comparison results for the volume of geodesic celestial spheres in Lorentzian manifolds. Zbl 1077.53056Díaz-Ramos, J. Carlos; García-Río, Eduardo; Hervella, Luis M. 1 2005 Four dimensional Osserman Lorentzian manifolds. Zbl 0856.53021García-Río, Eduardo; Kupeli, Demir N. 1 1996 Three-dimensional conformally symmetric manifolds. Zbl 1311.53057Calviño-Louzao, E.; García-Río, E.; Seoane-Bascoy, J.; Vázquez-Lorenzo, R. 1 2014 Locally conformally flat multidimensional cosmological models with a higher-dimensional external spacetime. Zbl 1078.83039Brozos-Vázquez, Miguel; García-Río, Eduardo; Vázquez-Lorenzo, Ramón 1 2005 Notes on harmonic tensor fields. Zbl 0940.53035García-Río, Eduardo; Vanhecke, Lieven; Vázquez-Abal, M. Elena 1 1999 Harmonic connections. Zbl 0881.53013García-Río, Eduardo; Vanhecke, Lieven; Vázquez-Abal, M. Elena 1 1996 Five-dimensional \(\varphi\)-symmetric spaces. Zbl 0889.53031García-Río, Eduardo; Vanhecke, Lieven 1 1996 Some splitting theorems for stably causal space-times. Zbl 0953.53040García-Río, Eduardo; Kupeli, Demir N. 1 1998 Conformal geometry of non-reductive four-dimensional homogeneous spaces. Zbl 1379.53047Calviño-Louzao, Esteban; García-Río, Eduardo; Gutiérrez-Rodríguez, Ixchel; Vázquez-Lorenzo, Ramón 1 2017 Algebraic properties of curvature operators in Lorentzian manifolds with large isometry groups. Zbl 1189.53070Calvaruso, Giovanni; García-Río, Eduardo 1 2010 Four-dimensional indefinite kähler Osserman manifolds. Zbl 1110.53052García-Río, Eduardo; Raki, Zoran; Vázquez-Abal, M. E. 1 2005 Local rigidity and nonrigidity of symplectic pairs. Zbl 1237.53026Calviño-Louzao, E.; García-Río, E.; Vázquez-Abal, M. E.; Vázquez-Lorenzo, R. 1 2012 Critical metrics and massive gravity solutions on three-dimensional Brinkmann waves. Zbl 07442583Brozos-Vázquez, M.; Caeiro-Oliveira, S.; García-Río, E. 1 2022 Three-dimensional homogeneous critical metrics for quadratic curvature functionals. Zbl 1480.53053Brozos-Vázquez, M.; García-Río, E.; Caeiro-Oliveira, S. 3 2021 Critical metrics for all quadratic curvature functionals. Zbl 1471.58016Brozos-Vázquez, Miguel; Caeiro-Oliveira, Sandro; García-Río, Eduardo 1 2021 Solutions to the affine quasi-Einstein equation for homogeneous surfaces. Zbl 1451.53051Brozos-Vázquez, M.; García-Río, E.; Gilkey, P.; Valle-Regueiro, X. 1 2020 Conformally Einstein and Bach-flat four-dimensional homogeneous manifolds. Zbl 1423.53057Calviño-Louzao, E.; García-Martínez, Xabier; García-Río, Eduardo; Gutiérrez-Rodríguez, Ixcheldzohara; Vázquez-Lorenzo, R. 2 2019 Isotropic quasi-Einstein manifolds. Zbl 1478.83009Brozos-Vázquez, M.; García-Río, E.; Valle-Regueiro, X. 1 2019 Constructing Bach flat manifolds of signature (2, 2) using the modified Riemannian extension. Zbl 1480.53061Calviño-Louzao, E.; García-Río, E.; Gilkey, P.; Gutiérrez-Rodríguez, I.; Vázquez-Lorenzo, R. 1 2019 Aspects of differential geometry IV. Zbl 1419.53002Calviño-Louzao, Esteban; García-Río, Eduardo; Gilkey, Peter; Park, JeongHyeong; Vázquez-Lorenzo, Ramón 1 2019 Homogeneous affine surfaces: affine Killing vector fields and gradient Ricci solitons. Zbl 1394.53021Brozos-Vázquez, Miguel; García-Río, Eduardo; Gilkey, Peter B. 13 2018 Half conformally flat generalized quasi-Einstein manifolds of metric signature \((2, 2)\). Zbl 1395.53040Brozos-Vázquez, Miguel; García-Río, Eduardo; Gilkey, Peter; Valle-Regueiro, Xabier 6 2018 The structure of the Ricci tensor on locally homogeneous Lorentzian gradient Ricci solitons. Zbl 1411.53036Brozos-Vázquez, M.; García-Río, E.; Gavino-Fernández, S.; Gilkey, P. 4 2018 Bach-flat isotropic gradient Ricci solitons. Zbl 1387.53058Calviño-Louzao, Esteban; García-Río, Eduardo; Gutiérrez-Rodríguez, Ixchel; Vázquez-Lorenzo, Ramón 3 2018 A natural linear equation in affine geometry: the affine quasi-Einstein equation. Zbl 1392.53056Brozos-Vázquez, Miguel; García-Río, Eduardo; Gilkey, Peter; Valle-Regueiro, Xabier 3 2018 Affine surfaces which are Kähler, para-Kähler, or nilpotent Kähler. Zbl 1400.53029Calviño-Louzao, E.; García-Río, E.; Gilkey, P.; Gutiérrez-Rodríguez, I.; Vázquez-Lorenzo, R. 3 2018 The affine quasi-Einstein equation for homogeneous surfaces. Zbl 1409.53037Brozos-Vázquez, M.; García-Río, E.; Gilkey, P.; Valle-Regueiro, X. 1 2018 Homogeneous Ricci almost solitons. Zbl 1402.53037Calviño-Louzao, Esteban; Fernández-López, Manuel; García-Río, Eduardo; Vázquez-Lorenzo, Ramón 11 2017 Aspects of differential geometry. III. Zbl 1371.53001Calviño-Louzao, Esteban; García-Río, Eduardo; Gilkey, Peter; Park, JeongHyeong; Vázquez-Lorenzo, Ramón 2 2017 Conformal geometry of non-reductive four-dimensional homogeneous spaces. Zbl 1379.53047Calviño-Louzao, Esteban; García-Río, Eduardo; Gutiérrez-Rodríguez, Ixchel; Vázquez-Lorenzo, Ramón 1 2017 On gradient Ricci solitons with constant scalar curvature. Zbl 1327.53057Fernández-López, Manuel; García-Río, Eduardo 15 2016 Homogeneous affine surfaces: moduli spaces. Zbl 1345.53015Brozos-Vázquez, M.; García-Río, E.; Gilkey, P. 8 2016 Half conformally flat gradient Ricci almost solitons. Zbl 1371.53024Brozos-Vázquez, M.; García-Río, E.; Valle-Regueiro, X. 4 2016 Four-dimensional neutral signature self-dual gradient Ricci solitons. Zbl 1358.53045García-Río, Eduardo; Brozos-Vázquez, Miguel 4 2016 Local structure of self-dual gradient Yamabe solitons. Zbl 1372.53070Brozos-Vázquez, Miguel; Calviño-Louzao, Esteban; García-Río, Eduardo; Vázquez-Lorenzo, Ramón 2 2016 Geometric properties of generalized symmetric spaces. Zbl 1335.53067Calviño-Louzao, Esteban; García-Río, Eduardo; Vázquez-Abal, María Elena; Vázquez-Lorenzo, Ramón 4 2015 Homothety curvature homogeneity and homothety homogeneity. Zbl 1343.53072García-Río, E.; Gilkey, P.; Nikčević, S. 3 2015 Homogeneity of Lorentzian three-manifolds with recurrent curvature. Zbl 1307.53057García-Río, Eduardo; Gilkey, Peter B.; Nikčević, Stana 11 2014 Locally conformally flat Lorentzian quasi-Einstein manifolds. Zbl 1291.53021Brozos-Vázquez, M.; García-Río, E.; Gavino-Fernández, S. 5 2014 A note on locally conformally flat gradient Ricci solitons. Zbl 1284.53046Fernández-López, Manuel; García-Río, Eduardo 4 2014 Three-dimensional conformally symmetric manifolds. Zbl 1311.53057Calviño-Louzao, E.; García-Río, E.; Seoane-Bascoy, J.; Vázquez-Lorenzo, R. 1 2014 Locally conformally flat Lorentzian gradient Ricci solitons. Zbl 1285.53059Brozos-Vázquez, M.; García-Río, E.; Gavino-Fernández, S. 32 2013 A sharp lower bound for the scalar curvature of certain steady gradient Ricci solitons. Zbl 1277.53041Fernández-López, Manuel; García-Río, Eduardo 2 2013 Applications of affine and Weyl geometry. Zbl 1273.53002García-Río, Eduardo; Gilkey, Peter; Nikčević, Stana; Vázquez-Lorenzo, Ramón 1 2013 Three-dimensional Lorentzian homogeneous Ricci solitons. Zbl 1264.53052Brozos-Vázquez, M.; Calvaruso, G.; García-Río, E. 41 2012 Some gap theorems for gradient Ricci solitons. Zbl 1247.53051Fernández-López, Manuel; García-Río, Eduardo 10 2012 A note on compact Cotton solitons. Zbl 1256.83023Calviño-Louzao, E.; García-Río, E.; Vázquez-Lorenzo, R. 7 2012 Higher-dimensional Osserman metrics with non-nilpotent Jacobi operators. Zbl 1237.53070Calviño-Louzao, E.; García-Río, E.; Gilkey, P.; Vázquez-Lorenzo, R. 5 2012 Curvature operators and generalizations of symmetric spaces in Lorentzian geometry. Zbl 1260.53122Calviño-Louzao, E.; García-Río, E.; Vázquez-Abal, M. E.; Vázquez-Lorenzo, R. 2 2012 Local rigidity and nonrigidity of symplectic pairs. Zbl 1237.53026Calviño-Louzao, E.; García-Río, E.; Vázquez-Abal, M. E.; Vázquez-Lorenzo, R. 1 2012 Geometric realizability of covariant derivative Kähler tensors for almost pseudo-Hermitian and almost para-Hermitian manifolds. Zbl 1331.53046Brozos-Vázquez, Miguel; García-Río, Eduardo; Gilkey, Peter; Hervella, Luis Maria 1 2012 Rigidity of shrinking Ricci solitons. Zbl 1226.53047Fernández-López, Manuel; García-Río, Eduardo 39 2011 Ricci solitons on Lorentzian manifolds with large isometry groups. Zbl 1266.53049Batat, W.; Brozos-Vázquez, M.; García-Río, E.; Gavino-Fernández, S. 23 2011 Maximum principles and gradient Ricci solitons. Zbl 1217.53042Fernández-López, Manuel; García-Río, Eduardo 13 2011 Riemann extensions of torsion-free connections with degenerate Ricci tensor. Zbl 1220.53026Calviño-Louzao, E.; García-Río, E.; Vázquez-Lorenzo, R. 10 2010 Diameter bounds and Hitchin-Thorpe inequalities for compact Ricci solitons. Zbl 1198.53035Fernández-López, Manuel; García-Río, Eduardo 7 2010 Four-dimensional Osserman metrics of neutral signature. Zbl 1186.53028García-Río, Eduardo; Gilkey, Peter B.; Vázquez-Abal, M. Elena; Vázquez-Lorenzo, Ramón 2 2010 Algebraic properties of curvature operators in Lorentzian manifolds with large isometry groups. Zbl 1189.53070Calvaruso, Giovanni; García-Río, Eduardo 1 2010 The geometry of Walker manifolds. Zbl 1206.53039Brozos-Vázquez, Miguel; García-Río, Eduardo; Gilkey, Peter; Nikčević, Stana; Vázquez-Lorenzo, Ramón 44 2009 The geometry of modified Riemannian extensions. Zbl 1186.53056Calviño-Louzao, E.; García-Río, E.; Gilkey, P.; Vázquez-Lorenzo, R. 24 2009 Four-dimensional Osserman metrics revisited. Zbl 1185.53052Calviño-Louzao, E.; García-Río, E.; Vázquez-Lorenzo, R. 1 2009 A remark on compact Ricci solitons. Zbl 1132.53023Fernández-López, M.; García-Río, E. 47 2008 Hermitian-Walker 4-manifolds. Zbl 1135.53049Davidov, J.; Díaz-Ramos, J. C.; García-Río, E.; Matsushita, Y.; Muškarov, O.; Vázquez-Lorenzo, R. 9 2008 Lorentzian 3-manifolds with commuting curvature operators. Zbl 1141.53319García-Río, Eduardo; Haji-Badali, Ali; Vázquez-Abal, M. Elena; Vázquez-Lorenzo, Ramón 9 2008 Lorentzian three-manifolds with special curvature operators. Zbl 1132.83014García-Río, E.; Badali, A. Haji; Vázquez-Lorenzo, R. 5 2008 Relating the curvature tensor and the complex Jacobi operator of an almost Hermitian manifold. Zbl 1180.53030Brozos-Vázquez, M.; García-Río, E.; Gilkey, P. 4 2008 Four-dimensional manifolds with degenerate self-dual Weyl curvature operator. Zbl 1181.53030Cortés-Ayaso, Alexandre; Díaz-Ramos, J. Carlos; García-Río, Eduardo 3 2008 Symplectic, Hermitian and Kähler structures on Walker 4-manifolds. Zbl 1173.53030García-Río, Eduardo; Haze, Seiya; Katayama, Noriaki; Matsushita, Yasuo 2 2008 Osserman and conformally Osserman manifolds with warped and twisted product structure. Zbl 1161.53025Brozos-Vázquez, Miguel; García-Río, Eduardo; Vázquez-Lorenzo, Ramón 2 2008 On the local geometry of three-dimensional Walker metrics. Zbl 1161.53353García-Río, E.; Haji-Badali, A.; Vázquez-Abal, M. E.; Vázquez-Lorenzo, R. 1 2008 Almost Kähler Walker 4-manifolds. Zbl 1106.53046Davidov, J.; Díaz-Ramos, J. C.; García-Río, E.; Matsushita, Y.; Muškarov, O.; Vázquez-Lorenzo, R. 13 2007 Four-dimensional Osserman-Ivanov-Petrova metrics of neutral signature. Zbl 1114.83300Calviño-Louzao, Esteban; García-Río, Eduardo; Vázquez-Lorenzo, Ramón 3 2007 Examples of signature \((2,2)\) manifolds with commuting curvature operators. Zbl 1129.53058Brozos-Vázquez, M.; García-Río, E.; Gilkey, P.; Vázquez-Lorenzo, R. 3 2007 Stanilov-Tsankov-Videv theory. Zbl 1133.53013Brozos-Vázquez, Miguel; Fiedler, Bernd; García-Río, Eduardo; Gilkey, Peter; Nikčević, Stana; Stanilov, Grozio; Tsankov, Yulian; Vázquez-Lorenzo, Ramón; Videv, Veselin 1 2007 Complete locally conformally flat manifolds of negative curvature. Zbl 1128.53018Brozos-Vázquez, Miguel; García-Río, Eduardo; Vázquez-Lorenzo, Ramón 7 2006 New examples of Osserman metrics with nondiagonalizable Jacobi operators. Zbl 1099.53047Díaz-Ramos, J. Carlos; García-Río, Eduardo; Vázquez-Lorenzo, Ramón 6 2006 Conformally Osserman four-dimensional manifolds whose conformal Jacobi operators have complex eigenvalues. Zbl 1149.53316Brozos-Vázquez, M.; García-Río, E.; Vázquez-Lorenzo, R. 6 2006 Osserman metrics on Walker 4-manifolds equipped with a para-Hermitian structure. Zbl 1152.53311Díaz-Ramon, J. Carlos; García-Río, Eduardo; Vázquez-Lorenzo, Ramón 2 2006 Three-dimensional Lorentz manifolds admitting a parallel null vector field. Zbl 1068.53049Chaichi, M.; García-Río, E.; Vásquez-Abal, M. E. 33 2005 Curvature properties of four-dimensional Walker metrics. Zbl 1086.83031Chaichi, M.; García-Río, E.; Matsushita, Y. 22 2005 Some remarks on locally conformally flat static space-times. Zbl 1076.53084Brozos-Vázquez, Miguel; García-Río, Eduardo; Vázquez-Lorenzo, Ramón 19 2005 Warped product metrics and locally conformally flat structures. Zbl 1098.53023Brozos-Vázquez, M.; García-Río, E.; Vázquez-Lorenzo, R. 4 2005 Total curvatures of geodesic spheres associated to quadratic curvature invariants. Zbl 1098.53026García-Río, Eduardo; Díaz-Ramos, J. Carlos.; Hervella, Luis 2 2005 Comparison results for the volume of geodesic celestial spheres in Lorentzian manifolds. Zbl 1077.53056Díaz-Ramos, J. Carlos; García-Río, Eduardo; Hervella, Luis M. 1 2005 Locally conformally flat multidimensional cosmological models with a higher-dimensional external spacetime. Zbl 1078.83039Brozos-Vázquez, Miguel; García-Río, Eduardo; Vázquez-Lorenzo, Ramón 1 2005 Four-dimensional indefinite kähler Osserman manifolds. Zbl 1110.53052García-Río, Eduardo; Raki, Zoran; Vázquez-Abal, M. E. 1 2005 A note on the structure of algebraic curvature tensors. Zbl 1056.53014Díaz-Ramos, J. Carlos; García-Río, Eduardo 3 2004 The structure of algebraic covariant derivative curvature tensors. Zbl 1080.53017Díaz-Ramos, J.; Fiedler, B.; García-Río, E.; Gilkey, P. 2 2004 On a differential equation characterizing Euclidean spheres. Zbl 1058.53027García-Río, Eduardo; Kupeli, Demir N.; Ünal, Bülent 16 2003 Characterizing specific Riemannian manifolds by differential equations. Zbl 1033.53033Erkekoğlu, Fazilet; García-Río, Eduardo; Kupeli, Demir N.; Ünal, Bülent 12 2003 On level sets of Lorentzian distance function. Zbl 1042.83006Erkekoğlu, F.; García-Río, E.; Kupeli, D. N. 7 2003 Osserman manifolds in semi-Riemannian geometry. Zbl 1005.53040García-Río, Eduardo; Kupeli, Demir N.; Vázquez-Lorenzo, Ramón 30 2002 Pseudo-Riemannian manifolds with simple Jacobi operators. Zbl 1042.53011Bonome, Agustin; Castro, Regina; García-Rio, Eduardo; Hervella, Luis; Vázquez-Lorenzo, Ramón 5 2002 A characterization of cosmological time functions. Zbl 1006.53058Fernández-López, Manuel; García-Río, Eduardo; Kupeli, Demir N. 1 2002 A curvature condition for a twisted product to be a warped product. Zbl 0999.53029Fernández-López, M.; García-Río, E.; Kupeli, D. N.; Ünal, B. 29 2001 Paraquaternionic Kähler manifolds. Zbl 0987.53020García-Río, Eduardo; Matsushita, Yasuo; Vázquez-Lorenzo, Ramón 10 2001 Four-dimensional Osserman symmetric spaces. Zbl 1008.53023García-Río, Eduardo; Vázquez-Lorenzo, Ramón 5 2001 Generalized Osserman four-dimensional manifolds. Zbl 1004.53049Bonome, Agustín; Castro, Paula; García-Río, Eduardo 2 2001 Isotropic Kähler structures on Engel 4-manifolds. Zbl 0964.53047García-Río, Eduardo; Matsushita, Yasuo 12 2000 Affine Osserman connections and their Riemann extensions. Zbl 0940.53017García-Río, Eduardo; Kupeli, Demir N.; Vázquez-Abal, M. Elena; Vázquez-Lorenzo, R. 19 1999 Semi-Riemannian maps and their applications. Zbl 0924.53003García-Río, Eduardo; Kupeli, Demir N. 14 1999 Notes on harmonic tensor fields. Zbl 0940.53035García-Río, Eduardo; Vanhecke, Lieven; Vázquez-Abal, M. Elena 1 1999 Nonsymmetric Osserman pseudo-Riemannian manifolds. Zbl 0939.53014García-Río, Eduardo; Vázquez-Abal, M. Elena; Vázquez-Lorenzo, R. 12 1998 Nonsymmetric Osserman indefinite Kähler manifolds. Zbl 0904.53022Bonome, Agustín; Castro, Regina; García-Río, Eduardo; Hervella, Luis M.; Vázquez-Lorenzo, R. 8 1998 On the paraholomorphic sectional curvature of almost para-Hermitian manifolds. Zbl 0965.53052Bonome, A.; Castro, R.; García-Río, E.; Hervella, L.; Vázquez-Lorenzo, R. 2 1998 Some splitting theorems for stably causal space-times. Zbl 0953.53040García-Río, Eduardo; Kupeli, Demir N. 1 1998 On a problem of Osserman in Lorentzian geometry. Zbl 0880.53017García-Río, Eduardo; Kupeli, Demir N.; Vázquez-Abal, M. Elena 17 1997 Curvature of indefinite almost contact manifolds. Zbl 1008.53032Bonome, Agustín; Castro, Regina; García-Río, Eduardo; Hervella, Luis 9 1997 Harmonic endomorphism fields. Zbl 0880.53032García-Río, Eduardo; Vanhecke, Lieven; Vázquez-Abal, M. Elena 9 1997 Pseudo-Chern classes and opposite Chern classes of indefinite almost Hermitian manifolds. Zbl 0923.53009Bonome, Agustín; Castro, Regina; García-Río, Eduardo; Hervella, Luis M.; Matsushita, Y. 4 1997 Geodesic transformations and space forms. Zbl 1076.53510García-Río, Eduardo; Vanhecke, Lieven 2 1997 Singularity versus splitting theorems for stably causal spacetimes. Zbl 0861.53064García-Río, Eduardo; Kupeli, Demir N. 11 1996 ...and 11 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 437 Authors 62 García-Río, Eduardo 44 Gilkey, Peter B. 35 Calvaruso, Giovanni 26 Vázquez-Lorenzo, Ramón 23 Brozos-Vázquez, Miguel 15 Calviño-Louzao, Esteban 14 Zaeim, Amirhesam 11 Bejan, Cornelia-Livia 10 Massamba, Fortuné 10 Vázquez Abal, María Elena 9 Deshmukh, Sharief 9 Haji-Badali, Ali 9 Matsushita, Yasuo 9 Nikčević, Stana Ž. 9 Pina, Romildo da Silva 9 Ṣahin, Bayram 9 Tadano, Homare 8 De, Uday Chand 8 Díaz-Ramos, José Carlos 8 Valle-Regueiro, Xabier 7 Davidov, Johann T. 7 Diallo, Abdoul Salam 7 Fernández-López, Manuel 7 Mantica, Carlo Alberto 6 Batat, Wafaa 6 Catino, Giovanni 6 Druţă-Romaniuc, Simona-Luiza 6 Kupeli, Demir N. 6 Mastrolia, Paolo 6 Molinari, Luca Guido 6 Wu, Jiayong 5 Cao, Huai-Dong 5 Galaev, Anton S. 5 Ghosh, Amalendu 5 Gutiérrez-Rodríguez, Ixchel 5 Gutiérrez, Manuel 5 Rigoli, Marco 5 Shenawy, Sameh 5 Stepanov, Sergeĭ Evgen’evich 5 Vîlcu, Gabriel Eduard 5 Zhang, Liangdi 4 Bidabad, Behroz 4 Blažić, Novica 4 Chen, Bang-Yen 4 Chudecki, Adam 4 Crâşmăreanu, Mircea 4 D’Ascanio, Daniela 4 de Leo, Barbara 4 Dunn, Corey M. 4 İşcan, Murat 4 Law, Peter R. 4 Mushkarov, Oleg K. 4 Pisani, Pablo A. G. 4 Seoane-Bascoy, Javier 4 Wu, Peng 3 Ali, Akram 3 Alías, Luis J. 3 Andrejić, Vladica 3 Atindogbe, Cyriaque 3 Azimpour, Sohrab 3 Chaichi, Mohamad 3 Chen, Qiang 3 Derdzinski, Andrzej 3 Dos Santos, João Paulo 3 Dunajski, Maciej 3 Gezer, Aydin 3 Gomes, José Nazareno Vieira 3 Güler, Sinem 3 Hervella, Luis M. 3 Ivanov, Stefan P. 3 Kowalski, Oldřich 3 Leandro, Benedito 3 Lee, Jaewon 3 Mikeš, Josef 3 Mondal, Chandan Kumar 3 Nadjafikhah, Mehdi 3 Perrone, Domenico 3 Rakić, Zoran 3 Ribeiro, Ernani jun. 3 Rimoldi, Michele 3 Schuller, Frederic P. 3 Shaikh, Absos Ali 3 Suh, Young Jin 3 Turanli, Sibel 3 Ünal, Bülent 3 Vanhecke, Lieven 3 Wohlfarth, Mattias N. R. 3 Wylie, William C. 3 Yang, Fei 2 Abbassi, Mohamed Tahar Kadaoui 2 Akbulut, Kursat 2 Amri, Noura 2 Aryanejad, Yadollah 2 Bastami, Milad 2 Blair, David E. 2 Bonome, Agustín 2 Caeiro-Oliveira, Sandro 2 Caldarella, Angelo V. 2 Castro Bolano, Regina 2 Chaubey, Sudhakar Kumar ...and 337 more Authors all top 5 Cited in 138 Serials 50 Journal of Geometry and Physics 37 Differential Geometry and its Applications 25 International Journal of Geometric Methods in Modern Physics 21 Annals of Global Analysis and Geometry 15 The Journal of Geometric Analysis 14 Journal of Mathematical Physics 14 Journal of Geometry 14 Results in Mathematics 13 Mediterranean Journal of Mathematics 11 Journal of Mathematical Analysis and Applications 11 Proceedings of the American Mathematical Society 11 Advances in Geometry 9 Nonlinear Analysis. Theory, Methods & Applications. 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