子流形几何中三类平行截面的关系及其应用  

The relations among three classes of parallel sections in submanifold geometry and its applications

作　　者：刘建成[1] 张德燕[1] 张秋燕[1] 

机构地区：[1]西北师范大学数学与信息科学学院,甘肃兰州730070

出　　处：《西北师范大学学报（自然科学版）》2006年第5期1-4,共4页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(10571129)

摘　　要：讨论常曲率空间Rn+p(c)中子流形上三类平行截面:平行平均曲率向量场、平行等参截面、平行脐截面三者之间的相互关系.证明了具有正截面曲率的紧致子流形上平行脐截面与平行等参截面的一个等价性定理,并通过反例说明截面曲率为正的条件是本质的.最后,给出了使截面曲率大于零的一个充分条件.The relations among three parallel sections, such as parallel mean curvature vector fields, parallel isoperimetrie section and parallel umblic section, on submanifolds in the constantly curved Riemannian manifolds ORn＋p（c） are studied. In particular, when the submanifolds are compact and have positive sectional curvature, an equivalent theorem about the parallel isoperimetric and the parallel umblic sections is proved. A counterexample is given in order to show the condition of the positive sectional curvature is essential. Finally, a sufficient condition ensuring the submanifolds have positive sectionalcurvature is obtained.

关 键 词：平行等参截面 平行脐截面 平行平均曲率向量场 截面曲率 

分 类 号：O186.12[理学—数学]