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Proceedings of the American Mathematical Society

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A short proof of Berger's curvature tensor estimates


Author: Hermann Karcher
Journal: Proc. Amer. Math. Soc. 26 (1970), 642-644
MSC: Primary 53.72
DOI: https://doi.org/10.1090/S0002-9939-1970-0270304-5
MathSciNet review: 0270304
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Abstract: A simple proof of Berger's estimate of the curvature tensor components in terms of the pinching is given and the result is extended to nonorthonormal arguments of the curvature tensor.


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

  • [1] M. Berger, Sur quelques variétés riemanniennes suffisamment pincées, Bull. Soc. Math. France 88 (1960), 57-71. MR 24 #A3606. MR 0133781 (24:A3606)
  • [2] S. I. Goldberg, Curvature and homology, Pure and Appl. Math., vol. XI, Academic Press, New York, 1962. MR 25 #2537. MR 0139098 (25:2537)
  • [3] D. Gromoll, W. Klingenberg and W. Meyer, Riemannsche Geometrie im Grossen, Lecture Notes in Math., no. 55, Springer-Verlag, Berlin and New York, 1968. MR 37 #4751. MR 0229177 (37:4751)
  • [4] G. Tsagas, A relation between Killing tensor fields and negative pinched Riemannian manifolds, Proc. Amer. Math. Soc. 22 (1969), 476-478. MR 39 #3429. MR 0242095 (39:3429)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0270304-5
Keywords: Curvature tensor identities, sectional curvature, pinching, curvature tensor norm, estimation of curvatures tensor components
Article copyright: © Copyright 1970 American Mathematical Society

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