伪欧氏空间的伪球面子流形  

PSEUDO-SPHERICAL SUBMANIFOLDS OF PSEUDO-EUCLIDEAN SPACE

作　　者：潘兴侠[1] 欧阳崇珍[1] 

机构地区：[1]南昌大学数学系,江西南昌330047

出　　处：《南昌大学学报（理科版）》2005年第3期211-214,共4页Journal of Nanchang University(Natural Science)

基　　金：国家自然科学基金资助项目(10261006);教育部优秀博士论文专项基金资助项目(200217);江西省自然科学基金资助项目(0211005)

摘　　要：将子流形的位置向量分解成水平分量和垂直分量,运用活动标架法研究伪欧氏空间的伪球面子流形。得到紧致类空子流形是伪球面子流形的两个充要条件:1)子流形的支撑函数是常值函数;2)子流形位置向量的水平分量是调和的。同时,给出具有平行平均曲率向量场的子流形是伪球面子流形的一个充要条件。特别地,对于Chen子流形,若它具有非迷向的平行平均曲率向量场且其支撑函数有固定符号,则它是伪球面子流形。Decomposing the position vectors of a submanifold into the tangential and normal components,the present paper studies the conditions under which a compact space-like submanifold of pseudo-Euclidean space is pseudo-spherical submanifold.It is observed that the tangential components of the position vectors being harmonic and the support function of the submanifold being contant provides two necessary and sufficient conditions.At the same time,we obtain another necessary and sufficient condition for the submanifold with parallel mean curvature vector.Specially,we also study Chen submanifold and obtain that if its mean curvature vector is parallel and not isotropic and the support function doesn't chang its sign,it is pseudo-spherical submanifold.

关 键 词：类空子流形 伪球面子流形 Chen子流形 平行平均曲率向量场 

分 类 号：O186[理学—数学]