Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

Journals Home Search My Subscriptions Subscribe
Previous issue | This issue | Most recent issue | All issues (1950–Present) | Next issue | Previous article | Articles in press | Recently published articles | Next article
Request Permissions
 
 

 

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
Full-text PDF Free Access

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.

References [Enhancements On Off] (What's this?)

  • [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.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 53C20

Retrieve articles in all journals with MSC: 53C20

Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0383295-8
Article copyright: © Copyright 1975 American Mathematical Society