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| SUBMANIFOLDS WITH NONNEGATIVE SECTIONAL CURVATURE |
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Citation： |
Shen yibing.SUBMANIFOLDS WITH NONNEGATIVE SECTIONAL CURVATURE[J].Chinese Annals of Mathematics B,1984,5(4):625~632 |
| Page view： 732
Net amount： 838 |
Authors： |
Shen yibing; |
Foundation： |
Projects Supported by the Science Fund of the Chinese Academg of Sciences. |
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| Abstract： |
This paper gives some sufficient conditions for a compact submanifold with nonnegative sectional curvature in a space form to be totally umbilical. In particular, for a compact submanifold M with flat normal bundle, if the scalar curvature is proportional to the mean curvature everywhere, then M is totally umbilical or the Riemannian product of several totally umbilical constantly curved submanifolds. |
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