# zbMATH — the first resource for mathematics

## Bishop, Richard L.

Compute Distance To:
 Author ID: bishop.richard-l Published as: Bishop, R.; Bishop, R. L.; Bishop, Richard; Bishop, Richard L. External Links: MGP · Wikidata · GND
 Documents Indexed: 48 Publications since 1963, including 4 Books
all top 5

#### Co-Authors

 11 single-authored 24 Alexander, Stephanie B. 8 Goldberg, Samuel I. 5 Berg, I. David 3 Crittenden, Richard J. 2 Ghrist, Robert W. 1 Menn, Michael 1 O’Neill, Barrett
all top 5

#### Serials

 4 Transactions of the American Mathematical Society 3 Geometriae Dedicata 3 Proceedings of the American Mathematical Society 2 American Mathematical Monthly 2 Advances in Mathematics 2 Illinois Journal of Mathematics 2 Indiana University Mathematics Journal 2 Journal of Differential Geometry 2 Manuscripta Mathematica 2 Michigan Mathematical Journal 2 Tohoku Mathematical Journal. Second Series 2 L’Enseignement Mathématique. 2e Série 1 Mathematics Magazine 1 Canadian Journal of Mathematics 1 Mathematische Annalen 1 Pacific Journal of Mathematics 1 Tensor. New Series 1 Annals of Global Analysis and Geometry 1 Differential Geometry and its Applications 1 Geometric and Functional Analysis. GAFA 1 Proceedings of the National Academy of Sciences of the United States of America 1 Communications in Analysis and Geometry 1 Regular and Chaotic Dynamics 1 Bulletin of the American Mathematical Society 1 International Electronic Journal of Geometry
all top 5

#### Fields

 35 Differential geometry (53-XX) 3 Convex and discrete geometry (52-XX) 2 Geometry (51-XX) 2 Manifolds and cell complexes (57-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Global analysis, analysis on manifolds (58-XX)

#### Citations contained in zbMATH

45 Publications have been cited 1,170 times in 1,078 Documents Cited by Year
Manifolds of negative curvature. Zbl 0191.52002
Bishop, R. L.; O’Neill, B.
1969
Geometry of manifolds. (Pure and Applied Mathematics. Vol. 15). Zbl 0132.16003
Bishop, R. L.; Crittenden, R. J.
1964
There is more than one way to frame a curve. Zbl 0298.53001
Bishop, Richard L.
1975
Tensor analysis on manifolds. Zbl 0218.53021
Bishop, R. L.; Goldberg, S. I.
1968
Geometry of manifolds. Reprint of the 1964 original. Zbl 0984.53001
Bishop, Richard L.; Crittenden, Richard J.
2001
On the second cohomology group of a Kaehler manifold of positive curvature. Zbl 0125.39403
Bishop, R. L.; Goldberg, S. I.
1965
The Hadamard-Cartan theorem in locally convex metric spaces. Zbl 0718.53055
Alexander, Stephanie B.; Bishop, Richard L.
1990
Some implications of the generalized Gauss-Bonnet theorem. Zbl 0133.15101
Bishop, R. L.; Goldberg, S. I.
1964
The Riemannian obstacle problem. Zbl 0625.53045
Alexander, Stephanie B.; Berg, I. David; Bishop, Richard L.
1987
Comparison theorems for curves of bounded geodesic curvature in metric spaces of curvature bounded above. Zbl 0859.53053
Alexander, Stephanie B.; Bishop, Richard L.
1996
Decomposition of cut loci. Zbl 0373.53019
Bishop, Richard L.
1977
Geometry of manifolds. Zbl 0146.43304
Bishop, R. L.; Crittenden, R. J.
1967
Curvature bounds for warped products of metric spaces. Zbl 1087.53064
Alexander, S. B.; Bishop, R. L.
2004
Geometric curvature bounds in Riemannian manifolds with boundary. Zbl 0793.53039
Alexander, Stephanie B.; Berg, I. David; Bishop, Richard L.
1993
Capture pursuit games on unbounded domains. Zbl 1177.91048
Alexander, S.; Bishop, R.; Ghrist, R.
2009
Total curvature and simple pursuit on domains of curvature bounded above. Zbl 1210.53008
Alexander, S.; Bishop, R.; Ghrist, R.
2010
Warped products of Hadamard spaces. Zbl 0909.53050
Alexander, Stephanie B.; Bishop, Richard L.
1998
Gauss equation and injectivity radii for subspaces in spaces of curvature bounded above. Zbl 1094.53073
Alexander, Stephanie B.; Bishop, Richard L.
2006
Infinitesimal convexity implies local convexity. Zbl 0268.53011
Bishop, Richard L.
1974
Characterizing motions by unit distance invariance. Zbl 0262.50001
Bishop, Richard L.
1973
On the topology of positively curved Kaehler manifolds. II. Zbl 0134.17906
Bishop, R. L.; Goldberg, S. I.
1965
Lorentz and semi-Riemannian spaces with Alexandrov curvature bounds. Zbl 1149.53040
Alexander, Stephanie B.; Bishop, Richard L.
2008
A cone splitting theorem for Alexandrov spaces. Zbl 1125.53023
Alexander, Stephanie B.; Bishop, Richard L.
2005
$$\mathcal FK$$-convex functions on metric spaces. Zbl 1020.53049
Alexander, Stephanie; Bishop, Richard L.
2003
Thin Riemannian manifolds with boundary. Zbl 0923.53013
Alexander, Stephanie B.; Bishop, Richard L.
1998
Clairaut submersions. Zbl 0246.53048
Bishop, R. L.
1972
The holonomy algebra of immersed manifolds of codimension two. Zbl 0177.50101
Bishop, R. L.
1968
On the topology of positively curved Kaehler manifolds. Zbl 0116.38802
Bishop, R. L.; Goldberg, S. I.
1963
On conformally flat spaces with commuting curvature and Ricci transformations. Zbl 0246.53046
Bishop, R. L.; Goldberg, S. I.
1972
The Fary-Milnor theorem in Hadamard manifolds. Zbl 0911.57007
Alexander, Stephanie B.; Bishop, Richard L.
1998
Infinitesimal convexity implies local convexity. Zbl 0281.53010
Bishop, Richard L.
1974
Spines and homology of thin Riemannian manifolds with boundary. Zbl 0992.53026
Alexander, Stephanie B.; Bishop, Richard L.
2000
Cauchy uniqueness in the Riemannian obstacle problem. Zbl 0621.53036
Alexander, Stephanie B.; Berg, I. David; Bishop, Richard L.
1986
A characterization of the Euclidean sphere. Zbl 0136.18703
Bishop, R. L.; Goldberg, S. I.
1966
Warped products admitting a curvature bound. Zbl 1352.53027
Alexander, Stephanie B.; Bishop, Richard L.
2016
Extrinsic curvature of semiconvex subspaces in Alexandrov geometry. Zbl 1190.53073
Alexander, Stephanie B.; Bishop, Richard L.
2010
The intrinsic geometry of a Jordan domain. Zbl 1170.53059
Bishop, Richard L.
2008
Circular billiard tables, conjugate loci, and a cardioid. Zbl 1023.37020
Bishop, R. L.
2003
Spines and topology of thin Riemannian manifolds. Zbl 1035.53047
Alexander, Stephanie B.; Bishop, Richard L.
2003
Racetracks and extremal problems for curves of bounded curvature in metric spaces. Zbl 0920.53019
Alexander, Stephanie B.; Bishop, Richard L.
1997
Convex-supporting domains on spheres. Zbl 0272.53026
Alexander, S.; Bishop, R. L.
1974
Cut loci, minimizers, and wavefronts in Riemannian manifolds with boundary. Zbl 0817.53023
Alexander, Stephanie B.; Berg, I. David; Bishop, Richard L.
1993
An infinitesimal cylindricity theorem. Zbl 0508.53059
Bishop, Richard L.
1982
Generic surfaces in $$E^4$$. Zbl 0295.53031
Bishop, Richard L.; Menn, Michael
1975
On curvature and Euler-Poincaré characteristic. Zbl 0173.49805
Bishop, R. L.; Goldberg, S. I.
1963
Warped products admitting a curvature bound. Zbl 1352.53027
Alexander, Stephanie B.; Bishop, Richard L.
2016
Total curvature and simple pursuit on domains of curvature bounded above. Zbl 1210.53008
Alexander, S.; Bishop, R.; Ghrist, R.
2010
Extrinsic curvature of semiconvex subspaces in Alexandrov geometry. Zbl 1190.53073
Alexander, Stephanie B.; Bishop, Richard L.
2010
Capture pursuit games on unbounded domains. Zbl 1177.91048
Alexander, S.; Bishop, R.; Ghrist, R.
2009
Lorentz and semi-Riemannian spaces with Alexandrov curvature bounds. Zbl 1149.53040
Alexander, Stephanie B.; Bishop, Richard L.
2008
The intrinsic geometry of a Jordan domain. Zbl 1170.53059
Bishop, Richard L.
2008
Gauss equation and injectivity radii for subspaces in spaces of curvature bounded above. Zbl 1094.53073
Alexander, Stephanie B.; Bishop, Richard L.
2006
A cone splitting theorem for Alexandrov spaces. Zbl 1125.53023
Alexander, Stephanie B.; Bishop, Richard L.
2005
Curvature bounds for warped products of metric spaces. Zbl 1087.53064
Alexander, S. B.; Bishop, R. L.
2004
$$\mathcal FK$$-convex functions on metric spaces. Zbl 1020.53049
Alexander, Stephanie; Bishop, Richard L.
2003
Circular billiard tables, conjugate loci, and a cardioid. Zbl 1023.37020
Bishop, R. L.
2003
Spines and topology of thin Riemannian manifolds. Zbl 1035.53047
Alexander, Stephanie B.; Bishop, Richard L.
2003
Geometry of manifolds. Reprint of the 1964 original. Zbl 0984.53001
Bishop, Richard L.; Crittenden, Richard J.
2001
Spines and homology of thin Riemannian manifolds with boundary. Zbl 0992.53026
Alexander, Stephanie B.; Bishop, Richard L.
2000
Warped products of Hadamard spaces. Zbl 0909.53050
Alexander, Stephanie B.; Bishop, Richard L.
1998
Thin Riemannian manifolds with boundary. Zbl 0923.53013
Alexander, Stephanie B.; Bishop, Richard L.
1998
The Fary-Milnor theorem in Hadamard manifolds. Zbl 0911.57007
Alexander, Stephanie B.; Bishop, Richard L.
1998
Racetracks and extremal problems for curves of bounded curvature in metric spaces. Zbl 0920.53019
Alexander, Stephanie B.; Bishop, Richard L.
1997
Comparison theorems for curves of bounded geodesic curvature in metric spaces of curvature bounded above. Zbl 0859.53053
Alexander, Stephanie B.; Bishop, Richard L.
1996
Geometric curvature bounds in Riemannian manifolds with boundary. Zbl 0793.53039
Alexander, Stephanie B.; Berg, I. David; Bishop, Richard L.
1993
Cut loci, minimizers, and wavefronts in Riemannian manifolds with boundary. Zbl 0817.53023
Alexander, Stephanie B.; Berg, I. David; Bishop, Richard L.
1993
The Hadamard-Cartan theorem in locally convex metric spaces. Zbl 0718.53055
Alexander, Stephanie B.; Bishop, Richard L.
1990
The Riemannian obstacle problem. Zbl 0625.53045
Alexander, Stephanie B.; Berg, I. David; Bishop, Richard L.
1987
Cauchy uniqueness in the Riemannian obstacle problem. Zbl 0621.53036
Alexander, Stephanie B.; Berg, I. David; Bishop, Richard L.
1986
An infinitesimal cylindricity theorem. Zbl 0508.53059
Bishop, Richard L.
1982
Decomposition of cut loci. Zbl 0373.53019
Bishop, Richard L.
1977
There is more than one way to frame a curve. Zbl 0298.53001
Bishop, Richard L.
1975
Generic surfaces in $$E^4$$. Zbl 0295.53031
Bishop, Richard L.; Menn, Michael
1975
Infinitesimal convexity implies local convexity. Zbl 0268.53011
Bishop, Richard L.
1974
Infinitesimal convexity implies local convexity. Zbl 0281.53010
Bishop, Richard L.
1974
Convex-supporting domains on spheres. Zbl 0272.53026
Alexander, S.; Bishop, R. L.
1974
Characterizing motions by unit distance invariance. Zbl 0262.50001
Bishop, Richard L.
1973
Clairaut submersions. Zbl 0246.53048
Bishop, R. L.
1972
On conformally flat spaces with commuting curvature and Ricci transformations. Zbl 0246.53046
Bishop, R. L.; Goldberg, S. I.
1972
Manifolds of negative curvature. Zbl 0191.52002
Bishop, R. L.; O’Neill, B.
1969
Tensor analysis on manifolds. Zbl 0218.53021
Bishop, R. L.; Goldberg, S. I.
1968
The holonomy algebra of immersed manifolds of codimension two. Zbl 0177.50101
Bishop, R. L.
1968
Geometry of manifolds. Zbl 0146.43304
Bishop, R. L.; Crittenden, R. J.
1967
A characterization of the Euclidean sphere. Zbl 0136.18703
Bishop, R. L.; Goldberg, S. I.
1966
On the second cohomology group of a Kaehler manifold of positive curvature. Zbl 0125.39403
Bishop, R. L.; Goldberg, S. I.
1965
On the topology of positively curved Kaehler manifolds. II. Zbl 0134.17906
Bishop, R. L.; Goldberg, S. I.
1965
Geometry of manifolds. (Pure and Applied Mathematics. Vol. 15). Zbl 0132.16003
Bishop, R. L.; Crittenden, R. J.
1964
Some implications of the generalized Gauss-Bonnet theorem. Zbl 0133.15101
Bishop, R. L.; Goldberg, S. I.
1964
On the topology of positively curved Kaehler manifolds. Zbl 0116.38802
Bishop, R. L.; Goldberg, S. I.
1963
On curvature and Euler-Poincaré characteristic. Zbl 0173.49805
Bishop, R. L.; Goldberg, S. I.
1963
all top 5

#### Cited by 1,299 Authors

 20 Siraj-Uddin 18 Farouki, Rida T. 13 Al-Solamy, Falleh Rijaullah 13 Korpinar, Talat 12 Bishop, Richard L. 11 Donnelly, Harold 10 Alexander, Stephanie B. 9 Ali, Akram 9 Eberlein, Patrick B. 8 Khan, Meraj Ali 8 Schröder, Viktor M. H. 8 Turhan, Essin 7 Gliklikh, Yuriĭ Evgen’evich 7 Lytchak, Alexander 6 Ehrlich, Paul Ewing 6 Goldberg, Samuel I. 6 Greene, Robert Everist 6 Han, Chang Yong 6 Petrunin, Anton Mikhailovich 6 Sestini, Alessandra 6 Takahashi, Masatomo 6 Ünal, Bülent 6 Yau, Shing-Tung 5 Anco, Stephen C. 5 Giannelli, Carlotta 5 Moore, John Douglas 5 Noronha, Maria Helena 5 Pişcoran, Laurian-Ioan 5 Sánchez Caja, Miguel 5 Shenawy, Sameh 5 Tanno, Shukichi 5 Yayli, Yusuf 4 Alkhaldi, Ali H. 4 Berestovskiĭ, Valeriĭ Nikolaevich 4 Chen, Bang-Yen 4 Chen, Su-Shing 4 Dobarro, Fernando Ruben 4 Gomes, José Nazareno Vieira 4 Gray, Alfred 4 Haji-Badali, Ali 4 Holopainen, Ilkka 4 Hurder, Steven E. 4 Kendall, Wilfrid S. 4 Loboda, Alexander Vasil’evich 4 Nešović, Emilija 4 Ni, Lei 4 Othman, Wan Ainun Mior 4 Ṣahin, Bayram 4 Shiohama, Katsuhiro 4 Stadler, Stephan 4 Wu, Hung-Hsi 4 Yamaguchi, Takao 3 Abresch, Uwe 3 Adachi, Toshiaki 3 Alghanemi, Azeb 3 Anderson, Michael T. 3 Atçeken, Mehmet 3 Ballmann, Hans Werner 3 Bangert, Victor 3 Borisenko, Aleksandr Andreevich 3 Cao, Huai-Dong 3 Clark, Alex 3 da Silva, Luiz Carlos Barbosa 3 Faghfouri, Morteza 3 Foertsch, Thomas 3 Galloway, Gregory J. 3 Goriely, Alain 3 Grant, James D. E. 3 Honda, Shun’ichi 3 Hui, Shyamal Kumar 3 Ibragimov, Gafurjan I. 3 Iliev, Bozhidar Zakhariev 3 Itokawa, Yoe 3 Jost, Jürgen 3 Kalish, Diane 3 Karp, Leon 3 Kasue, Atsushi 3 Kawakubo, Satoshi 3 Ketterer, Christian 3 Khan, Viqar Azam 3 Kisi, İlim 3 Kunzinger, Michael 3 Kuzminykh, Alexandr V. 3 Lohoué, Noël 3 Lumiste, Ülo 3 Meyer, Daniel 3 Miquel, Vicente 3 Naghi, Monia Fouad 3 Ontaneda, Pedro 3 Ozel, Cenap 3 Öztürk, Günay 3 Pahan, Sampa 3 Panoskaltsis, Vassilis P. 3 Panov, Dmitri Alekseevich 3 Petrov, Nikolaĭ Nikandrovich 3 Rapcsák, Tamás 3 Sakai, Takashi 3 Sakkalis, Takis 3 Sämann, Clemens 3 Sariaydin, Muhammed Talat ...and 1,199 more Authors
all top 5

#### Cited in 289 Serials

 52 Proceedings of the American Mathematical Society 50 Transactions of the American Mathematical Society 33 Journal of Geometry and Physics 28 Mathematische Annalen 27 Mathematische Zeitschrift 25 International Journal of Geometric Methods in Modern Physics 24 Geometriae Dedicata 22 The Journal of Geometric Analysis 20 Tohoku Mathematical Journal. Second Series 20 Differential Geometry and its Applications 17 Annals of Global Analysis and Geometry 16 Inventiones Mathematicae 15 Journal of Mathematical Analysis and Applications 15 Journal of Geometry 14 Journal of Functional Analysis 13 Advances in Mathematics 13 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 13 Archiv der Mathematik 12 General Relativity and Gravitation 12 Duke Mathematical Journal 11 Computer Aided Geometric Design 11 Geometry & Topology 11 Boletim da Sociedade Paranaense de Matemática. Terceira Série 10 Communications in Mathematical Physics 10 Compositio Mathematica 10 Siberian Mathematical Journal 9 International Journal of Theoretical Physics 9 Journal of Soviet Mathematics 9 Manuscripta Mathematica 8 Kodai Mathematical Journal 8 Bulletin of the American Mathematical Society 7 Mathematical Notes 7 Reports on Mathematical Physics 7 Annali di Matematica Pura ed Applicata. Serie Quarta 7 Journal of Mathematical Sciences (New York) 7 Kodai Mathematical Seminar Reports 6 Acta Mechanica 6 Archive for Rational Mechanics and Analysis 6 Israel Journal of Mathematics 6 Annales de l’Institut Fourier 6 Czechoslovak Mathematical Journal 6 Publications Mathématiques 6 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 6 Results in Mathematics 6 Calculus of Variations and Partial Differential Equations 6 Abstract and Applied Analysis 6 Mediterranean Journal of Mathematics 5 Periodica Mathematica Hungarica 5 Journal of Optimization Theory and Applications 5 Journal of the American Mathematical Society 5 Journal of Elasticity 5 Journal of the Egyptian Mathematical Society 5 Mathematical Problems in Engineering 5 Acta Mathematica Sinica. English Series 5 Dynamic Games and Applications 4 Computer Methods in Applied Mechanics and Engineering 4 Acta Mathematica 4 Journal of Differential Equations 4 Proceedings of the Japan Academy. Series A 4 Acta Applicandae Mathematicae 4 Physica D 4 Russian Mathematics 4 Turkish Journal of Mathematics 4 Journal of Inequalities and Applications 3 Journal of Computational Physics 3 Journal of Mathematical Physics 3 Reviews in Mathematical Physics 3 Chaos, Solitons and Fractals 3 Applied Mathematics and Computation 3 Automatica 3 Bulletin de la Société Mathématique de France 3 International Journal of Mathematics and Mathematical Sciences 3 Publications of the Research Institute for Mathematical Sciences, Kyoto University 3 Tokyo Journal of Mathematics 3 Topology and its Applications 3 Acta Mathematica Hungarica 3 Journal of Symbolic Computation 3 Revista Matemática Iberoamericana 3 Journal of Global Optimization 3 Annals of Physics 3 Linear Algebra and its Applications 3 Bulletin of the American Mathematical Society. New Series 3 St. Petersburg Mathematical Journal 3 Advances in Applied Clifford Algebras 3 Advances in Computational Mathematics 3 Annales Henri Poincaré 3 Journal of Nonlinear Mathematical Physics 3 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Bulletin of the Brazilian Mathematical Society. New Series 3 Proceedings of the Japan Academy 3 Advances in Mathematical Physics 3 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 3 Afrika Matematika 2 Journal of Applied Mathematics and Mechanics 2 Journal of Fluid Mechanics 2 Journal of Mathematical Biology 2 Letters in Mathematical Physics 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Physics Letters. A ...and 189 more Serials
all top 5

#### Cited in 56 Fields

 777 Differential geometry (53-XX) 201 Global analysis, analysis on manifolds (58-XX) 80 Partial differential equations (35-XX) 74 Manifolds and cell complexes (57-XX) 44 Dynamical systems and ergodic theory (37-XX) 43 Relativity and gravitational theory (83-XX) 37 Numerical analysis (65-XX) 33 Mechanics of deformable solids (74-XX) 31 Probability theory and stochastic processes (60-XX) 30 Calculus of variations and optimal control; optimization (49-XX) 30 Quantum theory (81-XX) 29 Several complex variables and analytic spaces (32-XX) 25 Convex and discrete geometry (52-XX) 24 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 22 Topological groups, Lie groups (22-XX) 22 Geometry (51-XX) 21 Mechanics of particles and systems (70-XX) 20 Algebraic topology (55-XX) 20 Computer science (68-XX) 18 Potential theory (31-XX) 17 Group theory and generalizations (20-XX) 15 Algebraic geometry (14-XX) 15 Operations research, mathematical programming (90-XX) 15 Systems theory; control (93-XX) 14 Ordinary differential equations (34-XX) 13 Fluid mechanics (76-XX) 12 Operator theory (47-XX) 10 Functions of a complex variable (30-XX) 10 Optics, electromagnetic theory (78-XX) 10 Biology and other natural sciences (92-XX) 9 General topology (54-XX) 8 Harmonic analysis on Euclidean spaces (42-XX) 8 Statistical mechanics, structure of matter (82-XX) 7 Linear and multilinear algebra; matrix theory (15-XX) 7 Abstract harmonic analysis (43-XX) 7 Statistics (62-XX) 6 Nonassociative rings and algebras (17-XX) 6 Real functions (26-XX) 6 Measure and integration (28-XX) 5 Information and communication theory, circuits (94-XX) 4 Functional analysis (46-XX) 3 History and biography (01-XX) 3 Approximations and expansions (41-XX) 2 General and overarching topics; collections (00-XX) 2 Number theory (11-XX) 2 Difference and functional equations (39-XX) 2 Integral transforms, operational calculus (44-XX) 2 Astronomy and astrophysics (85-XX) 1 Combinatorics (05-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Category theory; homological algebra (18-XX) 1 $$K$$-theory (19-XX) 1 Special functions (33-XX) 1 Sequences, series, summability (40-XX)

#### Wikidata Timeline

The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.