A finite version of Schur's theorem
Author:
R. S. Kulkarni
Journal:
Proc. Amer. Math. Soc. 53 (1975), 440-442
MSC:
Primary 53C20
DOI:
https://doi.org/10.1090/S0002-9939-1975-0383295-8
MathSciNet review:
0383295
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Abstract | References | Similar Articles | Additional Information
Abstract: A necessary and sufficient condition for constancy of curvature in terms of umbilicity of small metric spheres is given.
- [1] E. Cartan, Leçons sur la géométrie des espaces de Riemann, Gauthier-Villars, Paris, 1963.
- [2] Oldřich Kowalski, Properties of hypersurfaces which are characteristic for spaces of constant curvature, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 26 (1972), 233–245. MR 362156
- [3] Katsumi Nomizu, Generalized central spheres and the notion of spheres in Riemannian geometry, Tohoku Math. J. (2) 25 (1973), 129–137. MR 328798, https://doi.org/10.2748/tmj/1178241371
- [4] Dominic S. Leung and Katsumi Nomizu, The axiom of spheres in Riemannian geometry, J. Differential Geometry 5 (1971), 487–489. MR 290288
- [5] F. Schur, Über den Zusammenhang der Räume konstanten Krümmungsmasses mit den projectiven Räumen, Math. Ann. 27 (1886), 537-567.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1975-0383295-8
Article copyright:
© Copyright 1975
American Mathematical Society