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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1970-0270304-5
PII: S 0002-9939(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