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Gromoll, Detlef

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Author ID: gromoll.detlef Recent zbMATH articles by "Gromoll, Detlef"
Published as: Gromoll, D.; Gromoll, Detlef
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Documents Indexed: 35 Publications since 1966, including 3 Books

Publications by Year

Citations contained in zbMATH Open

34 Publications have been cited 1,445 times in 1,142 Documents Cited by Year
On the structure of complete manifolds of nonnegative curvature. Zbl 0246.53049
Cheeger, Jeff; Gromoll, Detlef
279
1972
The splitting theorem for manifolds of nonnegative Ricci curvature. Zbl 0223.53033
Cheeger, Jeff; Gromoll, Detlef
186
1971
Riemannsche Geometrie im Großen. Zbl 0155.30701
Gromoll, D.; Klingenberg, W.; Meyer, W.
156
1968
On differentiable functions with isolated critical points. Zbl 0212.28903
Gromoll, D.; Meyer, W.
129
1969
On complete open manifolds of positive curvature. Zbl 0191.19904
Gromoll, D.; Meyer, W.
95
1969
Periodic geodesics on compact Riemannian manifolds. Zbl 0203.54401
Gromoll, D.; Meyer, W.
82
1969
On complete manifolds with nonnegative Ricci curvature. Zbl 0704.53032
Abresch, Uwe; Gromoll, Detlef
54
1990
An exotic sphere with nonnegative sectional curvature. Zbl 0293.53015
Gromoll, Detlef; Meyer, Wolfgang
52
1974
Some relations betwee n the metric structure and the algebraic structure of the fundamental group in manifolds of nonpositive curvature. Zbl 0237.53037
Gromoll, Detlef; Wolf, Joseph A.
49
1971
Gauss parametrizations and rigidity aspects of submanifolds. Zbl 0588.53007
Dajczer, Marcos; Gromoll, Detlef
45
1985
The low-dimensional metric foliations of Euclidean spheres. Zbl 0683.53030
Gromoll, Detlef; Grove, Karsten
40
1988
Riemannsche Geometrie im Großen. 2. Aufl. Zbl 0293.53001
Gromoll, D.; Klingenberg, W.; Meyer, W.
36
1975
Metric foliations and curvature. Zbl 1163.53001
Gromoll, Detlef; Walschap, Gerard
35
2009
Real Kaehler submanifolds and uniqueness of the Gauss map. Zbl 0587.53051
Dajczer, Marcos; Gromoll, Detlef
32
1985
Differenzierbare Strukturen und Metriken positiver Krümmung auf Sphären. Zbl 0135.40301
Gromoll, D.
26
1966
A generalization of Berger’s rigidity theorem for positively curved manifolds. Zbl 0626.53032
Gromoll, Detlef; Grove, Karsten
21
1987
Rigidity of complete Euclidean hypersurfaces. Zbl 0667.53003
Dajczer, Marcos; Gromoll, Detlef
18
1990
On metrics on \(S^ 2\) all of whose geodesics are closed. Zbl 0477.53044
Gromoll, Detlef; Grove, Karsten
16
1981
One-dimensional metric foliations in constant curvature spaces. Zbl 0566.53035
Gromoll, Detlef; Grove, Karsten
15
1985
The Weierstrass representation for complete minimal real Kaehler submanifolds of codimension two. Zbl 0827.53047
Dajczer, Marcos; Gromoll, Detlef
13
1995
Nonnegatively curved metrics on \(S^{2}\times {\mathbb R}^{2}\). Zbl 1032.53030
Gromoll, Detlef; Tapp, Kristopher
9
2003
Examples of complete manifolds with positive Ricci curvature. Zbl 0583.53036
Gromoll, Detlef; Meyer, Wolfgang T.
8
1985
The structure of complete manifolds of nonnegative curvature. Zbl 0169.24101
Cheeger, J.; Gromoll, D.
8
1968
Euclidean hypersurfaces with isometric Gauss maps. Zbl 0562.53041
Dajczer, Marcos; Gromoll, Detlef
6
1986
On spherical submanifolds with nullity. Zbl 0565.53035
Dajczer, Marcos; Gromoll, Detlef
6
1985
On the lower bound for the injectivity radius of 1/4-pinched Riemannian manifolds. Zbl 0468.53035
Cheeger, Jeff; Gromoll, Detlef
6
1980
Isometric deformations of compact Euclidean submanifolds in codimension 2. Zbl 0857.53005
Dajczer, Marcos; Gromoll, Detlef
5
1995
The metric fibrations of Euclidean space. Zbl 1032.53026
Gromoll, Detlef; Walschap, Gerard
3
2001
Metric fibrations in Euclidean space. Zbl 0955.53015
Gromoll, Detlef; Walschap, Gerard
3
1997
Real Kaehler submanifolds in low codimension. Zbl 0894.53022
Dajczer, Marcos; Gromoll, Detlef
3
1997
On the almost negatively curved 3-sphere. Zbl 0651.53032
Buser, Peter; Gromoll, Detlef
3
1988
Rigidity of positively curved manifolds with large diameter. Zbl 0496.53028
Gromoll, Detlef; Grove, Karsten
3
1982
Complete minimal Kähler surfaces in \(\mathbb{R}^6\). Zbl 0894.53049
Dajczer, Marcos; Gromoll, Detlef
2
1997
Manifolds of nonnegative curvature. Zbl 0234.53044
Gromoll, Detlef
1
1971
Metric foliations and curvature. Zbl 1163.53001
Gromoll, Detlef; Walschap, Gerard
35
2009
Nonnegatively curved metrics on \(S^{2}\times {\mathbb R}^{2}\). Zbl 1032.53030
Gromoll, Detlef; Tapp, Kristopher
9
2003
The metric fibrations of Euclidean space. Zbl 1032.53026
Gromoll, Detlef; Walschap, Gerard
3
2001
Metric fibrations in Euclidean space. Zbl 0955.53015
Gromoll, Detlef; Walschap, Gerard
3
1997
Real Kaehler submanifolds in low codimension. Zbl 0894.53022
Dajczer, Marcos; Gromoll, Detlef
3
1997
Complete minimal Kähler surfaces in \(\mathbb{R}^6\). Zbl 0894.53049
Dajczer, Marcos; Gromoll, Detlef
2
1997
The Weierstrass representation for complete minimal real Kaehler submanifolds of codimension two. Zbl 0827.53047
Dajczer, Marcos; Gromoll, Detlef
13
1995
Isometric deformations of compact Euclidean submanifolds in codimension 2. Zbl 0857.53005
Dajczer, Marcos; Gromoll, Detlef
5
1995
On complete manifolds with nonnegative Ricci curvature. Zbl 0704.53032
Abresch, Uwe; Gromoll, Detlef
54
1990
Rigidity of complete Euclidean hypersurfaces. Zbl 0667.53003
Dajczer, Marcos; Gromoll, Detlef
18
1990
The low-dimensional metric foliations of Euclidean spheres. Zbl 0683.53030
Gromoll, Detlef; Grove, Karsten
40
1988
On the almost negatively curved 3-sphere. Zbl 0651.53032
Buser, Peter; Gromoll, Detlef
3
1988
A generalization of Berger’s rigidity theorem for positively curved manifolds. Zbl 0626.53032
Gromoll, Detlef; Grove, Karsten
21
1987
Euclidean hypersurfaces with isometric Gauss maps. Zbl 0562.53041
Dajczer, Marcos; Gromoll, Detlef
6
1986
Gauss parametrizations and rigidity aspects of submanifolds. Zbl 0588.53007
Dajczer, Marcos; Gromoll, Detlef
45
1985
Real Kaehler submanifolds and uniqueness of the Gauss map. Zbl 0587.53051
Dajczer, Marcos; Gromoll, Detlef
32
1985
One-dimensional metric foliations in constant curvature spaces. Zbl 0566.53035
Gromoll, Detlef; Grove, Karsten
15
1985
Examples of complete manifolds with positive Ricci curvature. Zbl 0583.53036
Gromoll, Detlef; Meyer, Wolfgang T.
8
1985
On spherical submanifolds with nullity. Zbl 0565.53035
Dajczer, Marcos; Gromoll, Detlef
6
1985
Rigidity of positively curved manifolds with large diameter. Zbl 0496.53028
Gromoll, Detlef; Grove, Karsten
3
1982
On metrics on \(S^ 2\) all of whose geodesics are closed. Zbl 0477.53044
Gromoll, Detlef; Grove, Karsten
16
1981
On the lower bound for the injectivity radius of 1/4-pinched Riemannian manifolds. Zbl 0468.53035
Cheeger, Jeff; Gromoll, Detlef
6
1980
Riemannsche Geometrie im Großen. 2. Aufl. Zbl 0293.53001
Gromoll, D.; Klingenberg, W.; Meyer, W.
36
1975
An exotic sphere with nonnegative sectional curvature. Zbl 0293.53015
Gromoll, Detlef; Meyer, Wolfgang
52
1974
On the structure of complete manifolds of nonnegative curvature. Zbl 0246.53049
Cheeger, Jeff; Gromoll, Detlef
279
1972
The splitting theorem for manifolds of nonnegative Ricci curvature. Zbl 0223.53033
Cheeger, Jeff; Gromoll, Detlef
186
1971
Some relations betwee n the metric structure and the algebraic structure of the fundamental group in manifolds of nonpositive curvature. Zbl 0237.53037
Gromoll, Detlef; Wolf, Joseph A.
49
1971
Manifolds of nonnegative curvature. Zbl 0234.53044
Gromoll, Detlef
1
1971
On differentiable functions with isolated critical points. Zbl 0212.28903
Gromoll, D.; Meyer, W.
129
1969
On complete open manifolds of positive curvature. Zbl 0191.19904
Gromoll, D.; Meyer, W.
95
1969
Periodic geodesics on compact Riemannian manifolds. Zbl 0203.54401
Gromoll, D.; Meyer, W.
82
1969
Riemannsche Geometrie im Großen. Zbl 0155.30701
Gromoll, D.; Klingenberg, W.; Meyer, W.
156
1968
The structure of complete manifolds of nonnegative curvature. Zbl 0169.24101
Cheeger, J.; Gromoll, D.
8
1968
Differenzierbare Strukturen und Metriken positiver Krümmung auf Sphären. Zbl 0135.40301
Gromoll, D.
26
1966
all top 5

Cited by 1,010 Authors

29 Dajczer, Marcos
20 Eschenburg, Jost-Hinrich
18 Long, Yiming
16 Su, Jiabao
16 Vlachos, Theodoros
14 Grove, Karsten
14 Shiohama, Katsuhiro
13 Wang, Wei
12 Walschap, Gerard
11 Mazzucchelli, Marco
11 Tanaka, Minoru
10 Bangert, Victor
10 Florit, Luis A.
10 Wei, Guofang
10 Wilhelm, Frederick H. jun.
9 Greene, Robert Everist
9 Guijarro, Luis
9 Noronha, Maria Helena
9 Wu, Hung-Hsi
8 Anderson, Michael T.
8 Duan, Huagui
8 Ehrlich, Paul Ewing
8 Gromoll, Detlef
8 Karcher, Hermann
8 Radeschi, Marco
8 Schröder, Viktor M. H.
8 Ziller, Wolfgang
7 DeVito, Jason
7 Durán Fernandez, Carlos Eduardo
7 Tojeiro, Ruy
7 Yau, Shing-Tung
6 Alexandrino, Marcos M.
6 Cao, Jianguo
6 Cingolani, Silvia
6 Galloway, Gregory J.
6 Ginzburg, Viktor L’vovich
6 Kaul, Helmut
6 Kondo, Kei-Ichi
6 Liu, Hui
6 Lu, Guangcun
6 Macarini, Leonardo
6 Marenich, Valery B.
6 Monod, Nicolas
6 Perrone, Domenico
6 Petersen, Peter V
6 Rong, Xiaochun
6 Sharafutdinov, Vladimir A.
6 Tapp, Kristopher
6 Tribuzy, Renato
6 Zheng, Fangyang
5 Asselle, Luca
5 Brendle, Simon
5 Cai, Mingliang
5 Calvaruso, Giovanni
5 Degiovanni, Marco
5 Dekster, Boris V.
5 Eberlein, Patrick B.
5 Innami, Nobuhiro
5 Kapovitch, Vitali
5 Maeda, Masao
5 Piccione, Paolo
5 Rodriguez, Lucio Ladislao
5 Savas-Halilaj, Andreas
5 Schoen, Richard Melvin
5 Searle, Catherine
5 Shioya, Takashi
5 Tam, Luen-Fai
4 Beem, John K.
4 Belegradek, Igor
4 Berestovskiĭ, Valeriĭ Nikolaevich
4 Buyalo, Sergei V.
4 Caprace, Pierre-Emmanuel
4 Cheeger, Jeff
4 Chen, Xiaoyang
4 Dai, Xianzhe
4 Darabi, Farhad
4 Galaz-Garcia, Fernando
4 Gürel, Basak Zehra
4 Henke, Wolfgang
4 Hingston, Nancy
4 Itokawa, Yoe
4 Javaloyes, Miguel Angel
4 Jost, Jürgen
4 Kasue, Atsushi
4 Kleinjohann, Norbert
4 Klingenberg, Wilhelm P. A.
4 Kurylev, Yaroslav V.
4 Lange, Christian
4 Lassas, Matti
4 Lee, Yong Hah
4 Li, Chong
4 Li, Shujie
4 Mendonça, Sergio J. X.
4 Moore, John Douglas
4 O’Sullivan, John J.
4 Rovenskiĭ, Vladimir Yuzefovich
4 Sakai, Takashi
4 Shen, Zhongmin
4 Sormani, Christina
4 Strake, Martin
...and 910 more Authors
all top 5

Cited in 188 Serials

64 Mathematische Zeitschrift
61 Mathematische Annalen
60 Proceedings of the American Mathematical Society
51 Transactions of the American Mathematical Society
44 Differential Geometry and its Applications
39 Annals of Global Analysis and Geometry
38 Manuscripta Mathematica
36 Inventiones Mathematicae
31 Geometriae Dedicata
28 Archiv der Mathematik
27 The Journal of Geometric Analysis
26 Advances in Mathematics
21 Duke Mathematical Journal
20 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
20 Tohoku Mathematical Journal. Second Series
19 Journal of Functional Analysis
19 Calculus of Variations and Partial Differential Equations
18 Journal of Geometry and Physics
17 Journal of Mathematical Analysis and Applications
14 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
13 Annali di Matematica Pura ed Applicata. Serie Quarta
13 Bulletin of the American Mathematical Society. New Series
13 Bulletin of the American Mathematical Society
12 Communications in Mathematical Physics
12 Siberian Mathematical Journal
11 Geometry & Topology
10 Acta Mathematica
10 Annales de l’Institut Fourier
9 Compositio Mathematica
9 Journal of Differential Equations
8 Mathematical Notes
8 Journal für die Reine und Angewandte Mathematik
8 Topology and its Applications
8 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
8 Journal of Mathematical Sciences (New York)
7 Bulletin de la Société Mathématique de France
7 Journal of Pure and Applied Algebra
7 Journal of Soviet Mathematics
7 Results in Mathematics
7 Journal of the American Mathematical Society
7 Journal de Mathématiques Pures et Appliquées. Neuvième Série
7 Annals of Mathematics. Second Series
7 Communications in Contemporary Mathematics
6 Mathematical Proceedings of the Cambridge Philosophical Society
6 International Journal of Mathematics
6 Geometric and Functional Analysis. GAFA
6 Algebraic & Geometric Topology
5 Ergodic Theory and Dynamical Systems
5 Comptes Rendus. Mathématique. Académie des Sciences, Paris
5 Kodai Mathematical Seminar Reports
5 Frontiers of Mathematics in China
4 General Relativity and Gravitation
4 Journal of Mathematical Physics
4 Illinois Journal of Mathematics
4 Michigan Mathematical Journal
4 Nagoya Mathematical Journal
4 Tokyo Journal of Mathematics
4 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
4 Boletim da Sociedade Brasileira de Matemática. Nova Série
4 Journal of the European Mathematical Society (JEMS)
3 Astrophysics and Space Science
3 Bulletin of the Australian Mathematical Society
3 Communications on Pure and Applied Mathematics
3 International Journal of Theoretical Physics
3 Israel Journal of Mathematics
3 Theoretical and Mathematical Physics
3 Commentarii Mathematici Helvetici
3 Journal of Geometry
3 Journal of Optimization Theory and Applications
3 Monatshefte für Mathematik
3 Proceedings of the Japan Academy. Series A
3 Rendiconti del Seminario Matematico della Università di Padova
3 Russian Mathematics
3 St. Petersburg Mathematical Journal
3 NoDEA. Nonlinear Differential Equations and Applications
3 Acta Mathematica Sinica. English Series
3 Bulletin of the Brazilian Mathematical Society. New Series
3 Journal of Fixed Point Theory and Applications
3 Journal of Topology and Analysis
2 Archive for Rational Mechanics and Analysis
2 Rocky Mountain Journal of Mathematics
2 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV
2 Mathematische Nachrichten
2 Proceedings of the London Mathematical Society. Third Series
2 Physica D
2 Optimization
2 Revista Matemática Iberoamericana
2 Communications in Partial Differential Equations
2 Expositiones Mathematicae
2 Acta Mathematica Sinica. New Series
2 Boletín de la Sociedad Matemática Mexicana. Third Series
2 Discrete and Continuous Dynamical Systems
2 Transformation Groups
2 Balkan Journal of Geometry and its Applications (BJGA)
2 Communications of the Korean Mathematical Society
2 Annales Henri Poincaré
2 Advances in Geometry
2 Journal of the Australian Mathematical Society
2 International Journal of Geometric Methods in Modern Physics
...and 88 more Serials
all top 5

Cited in 49 Fields

927 Differential geometry (53-XX)
246 Global analysis, analysis on manifolds (58-XX)
154 Manifolds and cell complexes (57-XX)
80 Partial differential equations (35-XX)
80 Dynamical systems and ergodic theory (37-XX)
36 Ordinary differential equations (34-XX)
33 Algebraic topology (55-XX)
30 Relativity and gravitational theory (83-XX)
28 Several complex variables and analytic spaces (32-XX)
24 Calculus of variations and optimal control; optimization (49-XX)
20 Potential theory (31-XX)
20 Convex and discrete geometry (52-XX)
19 Topological groups, Lie groups (22-XX)
18 Group theory and generalizations (20-XX)
12 Geometry (51-XX)
12 Quantum theory (81-XX)
10 Operator theory (47-XX)
9 Functional analysis (46-XX)
9 Mechanics of particles and systems (70-XX)
8 Functions of a complex variable (30-XX)
8 General topology (54-XX)
7 Real functions (26-XX)
6 Algebraic geometry (14-XX)
5 Category theory; homological algebra (18-XX)
5 Measure and integration (28-XX)
5 Probability theory and stochastic processes (60-XX)
5 Mechanics of deformable solids (74-XX)
5 Fluid mechanics (76-XX)
4 Number theory (11-XX)
4 Commutative algebra (13-XX)
4 Numerical analysis (65-XX)
3 General and overarching topics; collections (00-XX)
3 Abstract harmonic analysis (43-XX)
3 Statistics (62-XX)
3 Statistical mechanics, structure of matter (82-XX)
3 Operations research, mathematical programming (90-XX)
3 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
2 History and biography (01-XX)
2 Combinatorics (05-XX)
2 Associative rings and algebras (16-XX)
2 \(K\)-theory (19-XX)
2 Integral transforms, operational calculus (44-XX)
2 Astronomy and astrophysics (85-XX)
1 Linear and multilinear algebra; matrix theory (15-XX)
1 Nonassociative rings and algebras (17-XX)
1 Optics, electromagnetic theory (78-XX)
1 Geophysics (86-XX)
1 Biology and other natural sciences (92-XX)
1 Systems theory; control (93-XX)

Citations by Year

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