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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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

Abstract:

A necessary and sufficient condition for constancy of curvature in terms of umbilicity of small metric spheres is given.
References
    E. Cartan, Leçons sur la géométrie des espaces de Riemann, Gauthier-Villars, Paris, 1963.
  • 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.
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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