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| ON COMPLETE SPACE-LIKE SUBMANIFOLDS WITH PARALLELMEAN CURVATURE VECTOR |
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Citation： |
Shen Yibing,Dong Yuxing.ON COMPLETE SPACE-LIKE SUBMANIFOLDS WITH PARALLELMEAN CURVATURE VECTOR[J].Chinese Annals of Mathematics B,1998,19(3):369~380 |
| Page view： 1089
Net amount： 832 |
Authors： |
Shen Yibing; Dong Yuxing |
Foundation： |
Project supported by the National Natural Science
Foundation of China and the Natural Science Foundation of Zhejiang Province |
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| Abstract： |
Let $M^n$ be a complete space-like submanifold with parallel
mean curvature vector in an indefinite space form $N^{n+p}_p$(c).
A sharp estimate for the upper
bound of the norm of the second fundamental form of $M^n$ is obtained.
A generalization of this result to complete
space-like hypersurfaces with constant mean curvature in a Lorentz
manifold is given. Moreover, harmonic Gauss maps of $M^n$ in $N^{n
+p}_p(c)$ in a generalized sense are considered. |
Keywords： |
Pseudo-Riemannian manifold, Space-like submanifolds,
Parallel mean curvature vector, Second fundamental form |
Classification： |
53C40, 53C42 |
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