四元数射影空间中具有平行平均曲率向量的全实叶的Pinching定理(英文)  

A Pinching Theorem for Totally Real Riemannian Foliations with Parallelized Mean Curvature Vectors on a Quaternion Projective Space

作　　者：彭慧春[1] 李志波[2] 

机构地区：[1]华北电力大学数理系,北京102206 [2]郑州大学数学系,郑州450052

出　　处：《工程数学学报》2010年第5期932-938,共7页Chinese Journal of Engineering Mathematics

摘　　要：本文利用Nakagawa和Takagi的计算散度的方法,求出四元数射影空间上具有平行平均曲率向量的全实黎曼叶状结构F的向量场的散度,并证明了其上的一个Simons型的Pinching定理。By utilizing the divergence evaluation method of Nakagawa and Takagi for Harmonic foliations on the sphere,the divergence of a vector field on a totally real Riemannian foliation with parallelized mean curvature vectors on a quaternion projective space is found out.By pinching the length of the second fundamental form,a formula of Simons＇ type is obtained. The geometric restrictions of the length of the second fundamental form are proposed so that each leave of foliation is assumed to be totally umbilical.

关 键 词：黎曼叶状结构 四元数射影空间 平均曲率 散度 全脐 

分 类 号：O186[理学—数学]