工程数学学报
工程數學學報
공정수학학보
CHINESE JOURNAL OF ENGINEERING MATHEMATICS
2010年
5期
932-938
,共7页
黎曼叶状结构%四元数射影空间%平均曲率%散度%全脐
黎曼葉狀結構%四元數射影空間%平均麯率%散度%全臍
려만협상결구%사원수사영공간%평균곡솔%산도%전제
Riemannian foliations%quaternion projective space%mean curvature%divergence%totally umbilical
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.
本文利用Nakagawa和Takagi的計算散度的方法,求齣四元數射影空間上具有平行平均麯率嚮量的全實黎曼葉狀結構F的嚮量場的散度,併證明瞭其上的一箇Simons型的Pinching定理.
본문이용Nakagawa화Takagi적계산산도적방법,구출사원수사영공간상구유평행평균곡솔향량적전실려만협상결구F적향량장적산도,병증명료기상적일개Simons형적Pinching정리.
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.
