A finite version of Schur’s theorem
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- by R. S. Kulkarni
- Proc. Amer. Math. Soc. 53 (1975), 440-442
- DOI: https://doi.org/10.1090/S0002-9939-1975-0383295-8
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Abstract:
A necessary and sufficient condition for constancy of curvature in terms of umbilicity of small metric spheres is given.References
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- 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
- Katsumi Nomizu, Generalized central spheres and the notion of spheres in Riemannian geometry, Tohoku Math. J. (2) 25 (1973), 129–137. MR 328798, DOI 10.2748/tmj/1178241371
- Dominic S. Leung and Katsumi Nomizu, The axiom of spheres in Riemannian geometry, J. Differential Geometry 5 (1971), 487–489. MR 290288 F. Schur, Über den Zusammenhang der Räume konstanten Krümmungsmasses mit den projectiven Räumen, Math. Ann. 27 (1886), 537-567.
Bibliographic Information
- © Copyright 1975 American Mathematical Society
- 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