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 | References | Similar Articles | Additional Information
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.
- Marcel Berger, Sur quelques variétés riemanniennes suffisamment pincées, Bull. Soc. Math. France 88 (1960), 57–71 (French). MR 133781
- Samuel I. Goldberg, Curvature and homology, Pure and Applied Mathematics, Vol. XI, Academic Press, New York-London, 1962. MR 0139098
- D. Gromoll, W. Klingenberg, and W. Meyer, Riemannsche Geometrie im Grossen, Lecture Notes in Mathematics, No. 55, Springer-Verlag, Berlin-New York, 1968 (German). MR 0229177
- Grigorios Tsagas, A relation between Killing tensor fields and negative pinched Riemannian manifolds, Proc. Amer. Math. Soc. 22 (1969), 476–478. MR 242095, DOI https://doi.org/10.1090/S0002-9939-1969-0242095-7
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Additional Information
Keywords:
Curvature tensor identities,
sectional curvature,
pinching,
curvature tensor norm,
estimation of curvatures tensor components
Article copyright:
© Copyright 1970
American Mathematical Society