局部对称空间中具有平行平均曲率向量的子流形

On the Submanifolds with Parallel Mean Curvature Vector in Locally Symmetric Space

研究n+p维局部对称完备黎曼流形中具有平行平均曲率向量的n维紧致子流形,得到这类子流形关于第2基本形式模长平方的一个拼挤定理,推广了已有文献的一些结果。

This paper deals with the compact Submanifolds with parallel mean curvature in locally symmetric 8-pinching Riemannianifold. A pinching theorem on the square of the second fundamental length of this kind of Submanifolds is obtained and some results of Moxiao-huan have been generallized.