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Bishop, Richard L. (b. 1932 d. 2019)

Author ID: bishop.richard-l Recent zbMATH articles by "Bishop, Richard L."
Published as: Bishop, Richard L.; Bishop, R. L.; Bishop, R.
External Links: MGP · Wikidata · GND · IdRef
Documents Indexed: 49 Publications since 1963, including 4 Books and 1 Additional arXiv Preprint
Co-Authors: 7 Co-Authors with 37 Joint Publications
93 Co-Co-Authors

Publications by Year

Citations contained in zbMATH Open

45 Publications have been cited 1,684 times in 1,581 Documents Cited by Year
Manifolds of negative curvature. Zbl 0191.52002
Bishop, R. L.; O’Neill, B.
532
1969
Geometry of manifolds. Zbl 0132.16003
Bishop, R. L.; Crittenden, R. J.
332
1964
There is more than one way to frame a curve. Zbl 0298.53001
Bishop, Richard L.
256
1975
Tensor analysis on manifolds. Zbl 0218.53021
Bishop, R. L.; Goldberg, S. I.
78
1968
Geometry of manifolds. Reprint of the 1964 original. Zbl 0984.53001
Bishop, Richard L.; Crittenden, Richard J.
72
2001
On the second cohomology group of a Kaehler manifold of positive curvature. Zbl 0125.39403
Bishop, R. L.; Goldberg, S. I.
31
1965
Some implications of the generalized Gauss-Bonnet theorem. Zbl 0133.15101
Bishop, R. L.; Goldberg, S. I.
28
1964
The Hadamard-Cartan theorem in locally convex metric spaces. Zbl 0718.53055
Alexander, Stephanie B.; Bishop, Richard L.
25
1990
Clairaut submersions. Zbl 0246.53048
Bishop, R. L.
24
1972
Lorentz and semi-Riemannian spaces with Alexandrov curvature bounds. Zbl 1149.53040
Alexander, Stephanie B.; Bishop, Richard L.
23
2008
The Riemannian obstacle problem. Zbl 0625.53045
Alexander, Stephanie B.; Berg, I. David; Bishop, Richard L.
21
1987
Capture pursuit games on unbounded domains. Zbl 1177.91048
Alexander, S.; Bishop, R.; Ghrist, R.
19
2009
Decomposition of cut loci. Zbl 0373.53019
Bishop, Richard L.
19
1977
Geometric curvature bounds in Riemannian manifolds with boundary. Zbl 0793.53039
Alexander, Stephanie B.; Berg, I. David; Bishop, Richard L.
18
1993
Comparison theorems for curves of bounded geodesic curvature in metric spaces of curvature bounded above. Zbl 0859.53053
Alexander, Stephanie B.; Bishop, Richard L.
17
1996
Curvature bounds for warped products of metric spaces. Zbl 1087.53064
Alexander, S. B.; Bishop, R. L.
16
2004
Geometry of manifolds. Zbl 0146.43304
Bishop, R. L.; Crittenden, R. J.
15
1967
Gauss equation and injectivity radii for subspaces in spaces of curvature bounded above. Zbl 1094.53073
Alexander, Stephanie B.; Bishop, Richard L.
13
2006
Total curvature and simple pursuit on domains of curvature bounded above. Zbl 1210.53008
Alexander, S.; Bishop, R.; Ghrist, R.
12
2010
\(\mathcal FK\)-convex functions on metric spaces. Zbl 1020.53049
Alexander, Stephanie; Bishop, Richard L.
11
2003
On the topology of positively curved Kähler manifolds. II. Zbl 0134.17906
Bishop, R. L.; Goldberg, S. I.
9
1965
Warped products of Hadamard spaces. Zbl 0909.53050
Alexander, Stephanie B.; Bishop, Richard L.
9
1998
Characterizing motions by unit distance invariance. Zbl 0262.50001
Bishop, Richard L.
9
1973
A cone splitting theorem for Alexandrov spaces. Zbl 1125.53023
Alexander, Stephanie B.; Bishop, Richard L.
8
2005
The Fary-Milnor theorem in Hadamard manifolds. Zbl 0911.57007
Alexander, Stephanie B.; Bishop, Richard L.
8
1998
Infinitesimal convexity implies local convexity. Zbl 0281.53010
Bishop, Richard L.
8
1974
On conformally flat spaces with commuting curvature and Ricci transformations. Zbl 0246.53046
Bishop, R. L.; Goldberg, S. I.
7
1972
Infinitesimal convexity implies local convexity. Zbl 0268.53011
Bishop, Richard L.
7
1974
Extrinsic curvature of semiconvex subspaces in Alexandrov geometry. Zbl 1190.53073
Alexander, Stephanie B.; Bishop, Richard L.
6
2010
On the topology of positively curved Kaehler manifolds. Zbl 0116.38802
Bishop, R. L.; Goldberg, S. I.
6
1963
Thin Riemannian manifolds with boundary. Zbl 0923.53013
Alexander, Stephanie B.; Bishop, Richard L.
6
1998
The holonomy algebra of immersed manifolds of codimension two. Zbl 0177.50101
Bishop, R. L.
6
1968
A characterization of the Euclidean sphere. Zbl 0136.18703
Bishop, R. L.; Goldberg, S. I.
5
1966
The intrinsic geometry of a Jordan domain. Zbl 1170.53059
Bishop, Richard L.
4
2008
Cauchy uniqueness in the Riemannian obstacle problem. Zbl 0621.53036
Alexander, Stephanie B.; Berg, I. David; Bishop, Richard L.
4
1986
Warped products admitting a curvature bound. Zbl 1352.53027
Alexander, Stephanie B.; Bishop, Richard L.
3
2016
Spines and homology of thin Riemannian manifolds with boundary. Zbl 0992.53026
Alexander, Stephanie B.; Bishop, Richard L.
3
2000
Racetracks and extremal problems for curves of bounded curvature in metric spaces. Zbl 0920.53019
Alexander, Stephanie B.; Bishop, Richard L.
3
1997
Spines and topology of thin Riemannian manifolds. Zbl 1035.53047
Alexander, Stephanie B.; Bishop, Richard L.
3
2003
Circular billiard tables, conjugate loci, and a cardioid. Zbl 1023.37020
Bishop, R. L.
2
2003
Convex-supporting domains on spheres. Zbl 0272.53026
Alexander, S.; Bishop, R. L.
2
1974
Generic surfaces in \(E^4\). Zbl 0295.53031
Bishop, Richard L.; Menn, Michael
1
1975
Cut loci, minimizers, and wavefronts in Riemannian manifolds with boundary. Zbl 0817.53023
Alexander, Stephanie B.; Berg, I. David; Bishop, Richard L.
1
1993
An infinitesimal cylindricity theorem. Zbl 0508.53059
Bishop, Richard L.
1
1982
On curvature and Euler-Poincaré characteristic. Zbl 0173.49805
Bishop, R. L.; Goldberg, S. I.
1
1963
Warped products admitting a curvature bound. Zbl 1352.53027
Alexander, Stephanie B.; Bishop, Richard L.
3
2016
Total curvature and simple pursuit on domains of curvature bounded above. Zbl 1210.53008
Alexander, S.; Bishop, R.; Ghrist, R.
12
2010
Extrinsic curvature of semiconvex subspaces in Alexandrov geometry. Zbl 1190.53073
Alexander, Stephanie B.; Bishop, Richard L.
6
2010
Capture pursuit games on unbounded domains. Zbl 1177.91048
Alexander, S.; Bishop, R.; Ghrist, R.
19
2009
Lorentz and semi-Riemannian spaces with Alexandrov curvature bounds. Zbl 1149.53040
Alexander, Stephanie B.; Bishop, Richard L.
23
2008
The intrinsic geometry of a Jordan domain. Zbl 1170.53059
Bishop, Richard L.
4
2008
Gauss equation and injectivity radii for subspaces in spaces of curvature bounded above. Zbl 1094.53073
Alexander, Stephanie B.; Bishop, Richard L.
13
2006
A cone splitting theorem for Alexandrov spaces. Zbl 1125.53023
Alexander, Stephanie B.; Bishop, Richard L.
8
2005
Curvature bounds for warped products of metric spaces. Zbl 1087.53064
Alexander, S. B.; Bishop, R. L.
16
2004
\(\mathcal FK\)-convex functions on metric spaces. Zbl 1020.53049
Alexander, Stephanie; Bishop, Richard L.
11
2003
Spines and topology of thin Riemannian manifolds. Zbl 1035.53047
Alexander, Stephanie B.; Bishop, Richard L.
3
2003
Circular billiard tables, conjugate loci, and a cardioid. Zbl 1023.37020
Bishop, R. L.
2
2003
Geometry of manifolds. Reprint of the 1964 original. Zbl 0984.53001
Bishop, Richard L.; Crittenden, Richard J.
72
2001
Spines and homology of thin Riemannian manifolds with boundary. Zbl 0992.53026
Alexander, Stephanie B.; Bishop, Richard L.
3
2000
Warped products of Hadamard spaces. Zbl 0909.53050
Alexander, Stephanie B.; Bishop, Richard L.
9
1998
The Fary-Milnor theorem in Hadamard manifolds. Zbl 0911.57007
Alexander, Stephanie B.; Bishop, Richard L.
8
1998
Thin Riemannian manifolds with boundary. Zbl 0923.53013
Alexander, Stephanie B.; Bishop, Richard L.
6
1998
Racetracks and extremal problems for curves of bounded curvature in metric spaces. Zbl 0920.53019
Alexander, Stephanie B.; Bishop, Richard L.
3
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.
17
1996
Geometric curvature bounds in Riemannian manifolds with boundary. Zbl 0793.53039
Alexander, Stephanie B.; Berg, I. David; Bishop, Richard L.
18
1993
Cut loci, minimizers, and wavefronts in Riemannian manifolds with boundary. Zbl 0817.53023
Alexander, Stephanie B.; Berg, I. David; Bishop, Richard L.
1
1993
The Hadamard-Cartan theorem in locally convex metric spaces. Zbl 0718.53055
Alexander, Stephanie B.; Bishop, Richard L.
25
1990
The Riemannian obstacle problem. Zbl 0625.53045
Alexander, Stephanie B.; Berg, I. David; Bishop, Richard L.
21
1987
Cauchy uniqueness in the Riemannian obstacle problem. Zbl 0621.53036
Alexander, Stephanie B.; Berg, I. David; Bishop, Richard L.
4
1986
An infinitesimal cylindricity theorem. Zbl 0508.53059
Bishop, Richard L.
1
1982
Decomposition of cut loci. Zbl 0373.53019
Bishop, Richard L.
19
1977
There is more than one way to frame a curve. Zbl 0298.53001
Bishop, Richard L.
256
1975
Generic surfaces in \(E^4\). Zbl 0295.53031
Bishop, Richard L.; Menn, Michael
1
1975
Infinitesimal convexity implies local convexity. Zbl 0281.53010
Bishop, Richard L.
8
1974
Infinitesimal convexity implies local convexity. Zbl 0268.53011
Bishop, Richard L.
7
1974
Convex-supporting domains on spheres. Zbl 0272.53026
Alexander, S.; Bishop, R. L.
2
1974
Characterizing motions by unit distance invariance. Zbl 0262.50001
Bishop, Richard L.
9
1973
Clairaut submersions. Zbl 0246.53048
Bishop, R. L.
24
1972
On conformally flat spaces with commuting curvature and Ricci transformations. Zbl 0246.53046
Bishop, R. L.; Goldberg, S. I.
7
1972
Manifolds of negative curvature. Zbl 0191.52002
Bishop, R. L.; O’Neill, B.
532
1969
Tensor analysis on manifolds. Zbl 0218.53021
Bishop, R. L.; Goldberg, S. I.
78
1968
The holonomy algebra of immersed manifolds of codimension two. Zbl 0177.50101
Bishop, R. L.
6
1968
Geometry of manifolds. Zbl 0146.43304
Bishop, R. L.; Crittenden, R. J.
15
1967
A characterization of the Euclidean sphere. Zbl 0136.18703
Bishop, R. L.; Goldberg, S. I.
5
1966
On the second cohomology group of a Kaehler manifold of positive curvature. Zbl 0125.39403
Bishop, R. L.; Goldberg, S. I.
31
1965
On the topology of positively curved Kähler manifolds. II. Zbl 0134.17906
Bishop, R. L.; Goldberg, S. I.
9
1965
Geometry of manifolds. Zbl 0132.16003
Bishop, R. L.; Crittenden, R. J.
332
1964
Some implications of the generalized Gauss-Bonnet theorem. Zbl 0133.15101
Bishop, R. L.; Goldberg, S. I.
28
1964
On the topology of positively curved Kaehler manifolds. Zbl 0116.38802
Bishop, R. L.; Goldberg, S. I.
6
1963
On curvature and Euler-Poincaré characteristic. Zbl 0173.49805
Bishop, R. L.; Goldberg, S. I.
1
1963
all top 5

Cited by 1,786 Authors

39 Siraj-Uddin
26 Ali, Akram
19 Farouki, Rida T.
18 Korpinar, Talat
17 Khan, Meraj Ali
16 Al-Solamy, Falleh Rijaullah
15 Pal, Buddhadev
14 Pahan, Sampa
13 Shenawy, Sameh
12 Bhattacharyya, Arindam
12 Bishop, Richard L.
12 Ünal, Bülent
11 Alkhaldi, Ali Hussain
11 Donnelly, Harold
11 Othman, Wan Ainun Mior
10 Alexander, Stephanie B.
10 Hui, Shyamal Kumar
10 Lytchak, Alexander
10 Ozel, Cenap
9 Eberlein, Patrick B.
9 Kumar, Sangeet
9 Mustafa, Abdulqader
9 Naghi, Monia Fouad
9 Ṣahin, Bayram
9 Shahid, Mohammed Hasan
9 Taştan, Hakan Mete
9 Turhan, Essin
8 Chen, Bang-Yen
8 De, Uday Chand
8 Gliklikh, Yuriĭ Evgen’evich
8 Petrunin, Anton Mikhailovich
8 Pişcoran, Laurian-Ioan
8 Schröder, Viktor M. H.
8 Sharma, Anil
8 Solouma, Emad M.
8 Takahashi, Masatomo
8 Yayli, Yusuf
7 Al-Dayel, Ibrahim
7 Anco, Stephen C.
7 da Silva, Luiz Carlos Barbosa
7 Pal, Tanumoy
7 Siddiqui, Aliya Naaz
7 Srivastava, Sachin Kumar
7 Stadler, Stephan
6 Alluhaibi, Nadia
6 Alqahtani, Lamia Saeed
6 Aydin, Sibel Gerdan
6 Ehrlich, Paul Ewing
6 El-Sayied, Hoda Kamal Mohamed
6 Goldberg, Samuel I.
6 Gomes, José Nazareno Vieira
6 Greene, Robert Everist
6 Güler, Sinem
6 Haji-Badali, Ali
6 Ibragimov, Gafurjan I.
6 Kumar, Pankaj
6 Li, Yanlin
6 Loboda, Aleksandr Vasil’evich
6 Murathan, Cengizhan
6 Ni, Lei
6 Roy, Joydeb
6 Sestini, Alessandra
6 Yau, Shing-Tung
5 Abdel-Baky, Rashad A.
5 Ali, Rifaqat
5 Blaga, Adara-Monica
5 Dey, Santu
5 Giannelli, Carlotta
5 Han, Chang Yong
5 Hurder, Steven E.
5 Khan, Viqar Azam
5 Kumar, Anuj
5 Kunzinger, Michael
5 Lone, Mehraj Ahmad
5 Meena, Kiran
5 Mo, Xiaohuan
5 Mofarreh, Fatemah Y. Y.
5 Moore, John Douglas
5 Nešović, Emilija
5 Noronha, Maria Helena
5 Petersen, Peter V
5 Pigazzini, Alexander
5 Pruthi, Megha
5 Sánchez Caja, Miguel
5 Solis, Didier A.
5 Sormani, Christina
5 Syied, Noha
5 Tanno, Shukichi
5 Ünlütürk, Yasin
4 Alkhaldi, Ali H.
4 Atalay, Gülnur Şaffak
4 Atçeken, Mehmet
4 Beran, Tobias
4 Berestovskiĭ, Valeriĭ Nikolaevich
4 Bhunia, Nandan
4 Chen, Su-Shing
4 De Lima, Ronaldo Freire
4 Dobarro, Fernando Ruben
4 Ekici, Cumali
4 Elsharkawy, Ayman
...and 1,686 more Authors
all top 5

Cited in 365 Serials

55 Proceedings of the American Mathematical Society
52 Transactions of the American Mathematical Society
46 Journal of Geometry and Physics
45 International Journal of Geometric Methods in Modern Physics
33 The Journal of Geometric Analysis
31 Filomat
29 Mathematische Annalen
28 Geometriae Dedicata
28 Mathematische Zeitschrift
24 Tôhoku Mathematical Journal. Second Series
24 Differential Geometry and its Applications
20 Inventiones Mathematicae
20 Journal of Geometry
18 Journal of Mathematical Analysis and Applications
18 Boletim da Sociedade Paranaense de Matemática. Terceira Série
18 Mediterranean Journal of Mathematics
17 Annals of Global Analysis and Geometry
16 Journal of Functional Analysis
16 Results in Mathematics
14 General Relativity and Gravitation
13 Advances in Mathematics
13 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
13 Archiv der Mathematik
13 Duke Mathematical Journal
13 Computer Aided Geometric Design
13 Honam Mathematical Journal
13 Geometry & Topology
12 Turkish Journal of Mathematics
11 Communications in Mathematical Physics
11 Reports on Mathematical Physics
11 Manuscripta Mathematica
11 Journal of Mathematical Sciences (New York)
11 International Electronic Journal of Geometry
11 Advances in Mathematical Physics
10 Computer Methods in Applied Mechanics and Engineering
10 International Journal of Theoretical Physics
10 Compositio Mathematica
10 Siberian Mathematical Journal
10 Calculus of Variations and Partial Differential Equations
9 Annali di Matematica Pura ed Applicata. Serie Quarta
9 Journal of Soviet Mathematics
8 Mathematical Methods in the Applied Sciences
8 Annales de l’Institut Fourier
8 Journal of Optimization Theory and Applications
8 Kodai Mathematical Journal
8 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
8 Mathematical Problems in Engineering
8 Acta Mathematica Sinica. English Series
8 Bulletin of the American Mathematical Society
8 Afrika Matematika
7 Archive for Rational Mechanics and Analysis
7 Mathematical Notes
7 Physica D
7 Abstract and Applied Analysis
7 Journal of Inequalities and Applications
7 Hacettepe Journal of Mathematics and Statistics
7 Kodai Mathematical Seminar Reports
7 Asian-European Journal of Mathematics
7 Dynamic Games and Applications
7 AIMS Mathematics
6 Acta Mechanica
6 Israel Journal of Mathematics
6 Letters in Mathematical Physics
6 Czechoslovak Mathematical Journal
6 Publications Mathématiques
6 Mathematische Nachrichten
6 Journal of Elasticity
6 Proceedings of the National Academy of Sciences, India. Section A. Physical Sciences
6 Journal of Dynamical Systems and Geometric Theories
5 Periodica Mathematica Hungarica
5 Chaos, Solitons and Fractals
5 Journal of the London Mathematical Society. Second Series
5 Topology and its Applications
5 Bulletin of the Korean Mathematical Society
5 Facta Universitatis. Series Mathematics and Informatics
5 Journal of the American Mathematical Society
5 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
5 SIAM Journal on Optimization
5 Russian Mathematics
5 Journal of the Egyptian Mathematical Society
5 Arab Journal of Mathematical Sciences
5 Communications of the Korean Mathematical Society
4 Journal of Computational Physics
4 Journal of Mathematical Physics
4 Acta Mathematica
4 Automatica
4 Journal of Computational and Applied Mathematics
4 Journal of Differential Equations
4 Journal of Differential Geometry
4 Journal für die Reine und Angewandte Mathematik
4 Pacific Journal of Mathematics
4 Proceedings of the Japan Academy. Series A
4 Acta Applicandae Mathematicae
4 Discrete & Computational Geometry
4 Geometric and Functional Analysis. GAFA
4 Annals of Physics
4 Journal of Nonlinear Science
4 Potential Analysis
4 St. Petersburg Mathematical Journal
4 Advances in Computational Mathematics
...and 265 more Serials
all top 5

Cited in 58 Fields

1,192 Differential geometry (53-XX)
253 Global analysis, analysis on manifolds (58-XX)
111 Partial differential equations (35-XX)
96 Manifolds and cell complexes (57-XX)
67 Relativity and gravitational theory (83-XX)
56 Dynamical systems and ergodic theory (37-XX)
55 Numerical analysis (65-XX)
50 Mechanics of deformable solids (74-XX)
46 Several complex variables and analytic spaces (32-XX)
44 Calculus of variations and optimal control; optimization (49-XX)
40 Quantum theory (81-XX)
39 Geometry (51-XX)
37 Probability theory and stochastic processes (60-XX)
34 Topological groups, Lie groups (22-XX)
33 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
31 Convex and discrete geometry (52-XX)
31 Mechanics of particles and systems (70-XX)
28 Computer science (68-XX)
24 Algebraic geometry (14-XX)
24 Algebraic topology (55-XX)
23 Operations research, mathematical programming (90-XX)
22 Potential theory (31-XX)
21 Group theory and generalizations (20-XX)
20 Fluid mechanics (76-XX)
19 Ordinary differential equations (34-XX)
18 Systems theory; control (93-XX)
16 Operator theory (47-XX)
14 Optics, electromagnetic theory (78-XX)
14 Biology and other natural sciences (92-XX)
12 Linear and multilinear algebra; matrix theory (15-XX)
12 Measure and integration (28-XX)
11 General topology (54-XX)
11 Statistics (62-XX)
10 Functions of a complex variable (30-XX)
10 Harmonic analysis on Euclidean spaces (42-XX)
10 Statistical mechanics, structure of matter (82-XX)
9 Nonassociative rings and algebras (17-XX)
9 Real functions (26-XX)
8 Abstract harmonic analysis (43-XX)
7 Functional analysis (46-XX)
5 Combinatorics (05-XX)
4 General and overarching topics; collections (00-XX)
4 History and biography (01-XX)
4 Information and communication theory, circuits (94-XX)
3 Difference and functional equations (39-XX)
3 Approximations and expansions (41-XX)
2 Mathematical logic and foundations (03-XX)
2 Number theory (11-XX)
2 \(K\)-theory (19-XX)
2 Special functions (33-XX)
2 Integral transforms, operational calculus (44-XX)
2 Astronomy and astrophysics (85-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 Integral equations (45-XX)
1 Geophysics (86-XX)

Citations by Year

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