Scalar curvature, inequality and submanifold-Reference-Cited by-同舟云学术

Scalar curvature, inequality and submanifold

Published:1973 Issue:3 Volume:38 Page:605-608
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Chen Bang-yen,Okumura Masafumi

Abstract

Using an inequality relation between scalar curvature and length of second fundamental form, we may conclude that a submanifold must have nonnegative (or positive) sectional curvatures. An application to compact submanifolds in obtained.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1973-038-03/S0002-9939-1973-0343217-0/S0002-9939-1973-0343217-0.pdf

Reference5 articles.

1. On the mean curvature of submanifolds of euclidean space;Chen, Bang-yen;Bull. Amer. Math. Soc.,1971

2. Minimal submanifolds of a sphere with second fundamental form of constant length;Chern, S. S.,1970

3. Hypersurfaces and a pinching problem on the second fundamental tensor;Okumura, Masafumi;Amer. J. Math.,1974

4. \bysame, Submanifolds and a pinching problem on the second fundamental tensor (to appear).

5. Submanifolds of constant mean curvature;Smyth, Brian;Math. Ann.,1973

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