The DOI matches its Crossref record; 9 of the 9 references it cites were found in a registry or an index.
A Generalized Sphere Theorem
Abstract
A basic problem in Riemannian geometry is the study of relations between the topological structure and the Riemannian structure of a complete, connected Riemannian manifold M of dimension n > 2. By a classical theorem of Myers [10] such a manifold is compact if the sectional curvature K of M satisfies K > a > O. More precisely, the diameter d(M) of M satisfies d(M) < zc/< 8 . After the pioneering work of Rauch [11] the following result, known as the sphere theorem, was proved first by Berger [1] in even dimensions and finally by Klingenberg [8] as stated.
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Citations
Cites
Comparison Theorems in Riemannian Geometry
Cheeger, J., & Ebin, D. (2008) · American Mathematical Society eBooks · doi:10.1090/chel/365 · Cited by 970
Kervaire, M. A., & Milnor, J. W. (1963) · The Annals of Mathematics · doi:10.2307/1970128 · Cited by 904
Bishop, R., & Crittenden, R. (2001) · American Mathematical Society eBooks · doi:10.1090/chel/344 · Cited by 780
Generalized Poincare's Conjecture in Dimensions Greater Than Four
Smale, S. (1961) · The Annals of Mathematics · doi:10.2307/1970239 · Cited by 428
Riemannsche Geometrie im Großen
Gromoll, D., Meyer, W., & Klingenberg, W. (1975) · Lecture Notes in Mathematics · doi:10.1007/bfb0079185 · Cited by 357
How to conjugateC 1-close group actions
Grove, K., & Karcher, H. (1973) · Mathematische Zeitschrift · doi:10.1007/bf01214029 · Cited by 151
Self-citationA Contribution to Differential Geometry in the Large
Rauch, H. E. (1951) · The Annals of Mathematics · doi:10.2307/1969309 · Cited by 135
Über Riemannsche Mannigfaltigkeiten mit positiver Krümmung
Klingenberg, W. (1961) · Commentarii Mathematici Helvetici · doi:10.1007/bf02567004 · Cited by 132
The diameter of $\delta $-pinched manifolds
Shiohama, K. (1971) · Journal of Differential Geometry · doi:10.4310/jdg/1214429778 · Cited by 12
Self-citation
Cited by
Riemannian center of mass and mollifier smoothing
Karcher, H. (1977) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.3160300502 · Cited by 995
Chazal, F., & Lieutier, A. (2005) · Proceedings of the twenty-first annual symposium on Computational geometry · doi:10.1145/1064092.1064132 · Cited by 67
Diameter-extremal subsets of spheres
Katz, M. (1989) · Discrete & Computational Geometry · doi:10.1007/bf02187719 · Cited by 12
Metadata
- Authors
- Grove, K., & Shiohama, K.
- Venue
- The Annals of Mathematics
- Publisher
- JSTOR
- Published
- 1977-07
- Volume
- 106
- Issue
- 1
- Pages
- 201
- ISSN
- 0003-486X (ISSN-L)
- OpenAlex
- W2088604891
- Cited by
- 286
- References
- 9
- FWCI
- 1.95
- Type
- journal article
- Language
- en
- Open access
- closed
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