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Proceedings of the American Mathematical Society

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A finite version of Schur's theorem

Author: R. S. Kulkarni
Journal: Proc. Amer. Math. Soc. 53 (1975), 440-442
MSC: Primary 53C20
MathSciNet review: 0383295
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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 [Enhancements On Off] (What's this?)

  • [1] E. Cartan, Leçons sur la géométrie des espaces de Riemann, Gauthier-Villars, Paris, 1963.
  • [2] O. Kowalski, Properties of hypersurfaces, Ann. Sci. Norm. Sup. Pisa 26 (1972), 223-245. MR 0362156 (50:14598)
  • [3] K. Nomizu, Generalized central spheres, Tôhoku Math. J. 25 (1973), 129-137. MR 0328798 (48:7140)
  • [4] D. S. Leung and K. Nomizu, The axiom of spheres in Riemannian geometry, J. Differential Geometry 5 (1971), 487-489. MR 44 #7472. MR 0290288 (44:7472)
  • [5] F. Schur, Über den Zusammenhang der Räume konstanten Krümmungsmasses mit den projectiven Räumen, Math. Ann. 27 (1886), 537-567.

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