局部对称伪黎曼流形中的伪脐类空子流形

摘要: 研究局部对称伪黎曼流形N_p^n+p中的伪脐类空子流形Mⁿ.当Mⁿ是完备非紧且具有平行平均曲率向量场时，得到Mⁿ的第二基本形式的模长平方的一个拼挤定理.当Mⁿ是紧致且具有平行平均曲率向量场时，证得Mⁿ是全测地的.
- 伪黎曼流形 /
- 平行平均曲率向量场 /
- 伪脐 /
- 第二基本形式
Abstract: In this paper, we study the pseudo-umbilical space-like submanifolds Mⁿ which are immersed into locally symmetric pseudo-Riemannian manifolds N_p^n+p. When Mⁿ is complete non-compact and has a parallel mean curvature vector field, a pinching theorem for the square length of the second fundamental form of Mⁿ is obtained. When Mⁿ is compact and has a parallel mean curvature vector field, then we prove that Mⁿ is totally geodesic.
- pseudo-Riemannian manifold /
- parallel mean curvature field /
- pseudoumbilical /
- second fundamental form

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参考文献(16)

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