法联络平坦子流形与第二基本张量

Submanifolds with Flat Connection of Normal Bundle and the Second Fundamental Tensors

中文关键词:  子流形  局部对称  共形平坦

英文关键词:submanifold  locally symmetric  conformally flat.

中文摘要:

      本文首先将常曲率黎曼流形中Ｂ．Ｙ．Ｃｈｅｎ和Ｍ．Ｏｋｕｍｕｒａ关于数量曲率和截面曲率关系间的一个著名不等式推广到环绕空间是局部对称共形平坦黎曼流形的情形．作为应用，较简捷地将Ｍ．Ｏｋｕｍｕｒａ在［２］，［３］中的结果推广到这种环绕空间中法联络是平坦的子流形上去．

英文摘要:

      An inequality of B.Y.Chen and M.Okumura in constant curvature Riemannian maniffold is generalized to submanifold in a locally symmetric and conformally flat Riemannian manifold. As an application, the theorems of M.Okumura in [2],[3] are generalized and improved.