复射影空间中具有平行平均曲率向量的全实叶的Pinching定理

A PINCHING THEOREM ABOUT THE TOTALLY REAL FOLIATIONS WITH PARALLEL MEAN CURVATURE ON A COMPLEX PROJECTIVE SPACE

本文研究了复射影空间中具有平行平均曲率向量的黎曼叶状结构F.利用Nakagawa和Takagi的计算散度的方法,得到了复射影空间中具有平行平均曲率向量的黎曼叶状结构F上向量场的散度,证明了其上的一个整体Pinching定理,从而将复射影空间中任何具有极小法平面场的调和叶的性质推广到复射影空间中具有平行平均曲率向量的黎曼叶状结构F上.

The article discusses the totally real foliations with parallel mean curvature on a complex projective space. By using the method of Nakagawa and Takagi, the divergence of the vector field is found out, and a Pinching theorem about Ricci curvature of is obtained. A geometric property of Riemannian foliations with parallel mean curvature on a complex projective soace is proved.