某些黎曼流形中的全脐子流形

The main result obtaind in this paper is that :Let M be a totally umbilical submanifolds in Riemannian manifold N. If the Weyl conformal curvature tensor for N satisfies the following condition: ▽_xC=ω(X)C, for some 1-form ω and any vector field X in M, then M is con-formally flat or it is totally geodesic .     

拟常曲率黎曼流形中具有平行平均曲率向量的子流形

讨论了拟常曲黎曼流形中具有平行平均曲率向量的等距浸入子流形，给出了一个积分不等式，推广和改进献[1，2]的结果。