复射影空间和四元数射影空间中一类平均曲率向量平行的子流形

A CLASS OF SUBMANIFOLDS WITH PARALLEL MEAN CURVATURE VECTOR IN COMPLEX PRO.TECTIVE SPACES AND QUATERNION PROJECTIVE SPACES

本文利用Riemann submersion研究了复射影空间和四元数射影空间中一类平均曲率向量平行的子流形,得到了两个关于数量曲率和平均曲率的Pinching定理。

In this paper,a class of submanifolds with parallel mean curvature vector in complex projective spaces and quaternion projective spaces is studied by using Riemannian submersion. Two pinching theorems on scalar curvature and mean curvature are obtained.