伪黎曼空间形式中完备类空子流形的余维数约化  

Reduction of Codimension of Complete Spacelike Submanifolds in Semi-Rimannian Space Forms

作　　者：田小强 董丹 TIAN Xiao-qiang;DONG Dan(College of Basic,Beijing Polytechnic,Beijing 100176,China;College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]北京电子科技职业学院基础学院,北京100176 [2]西北师范大学数学与统计学院,兰州730070

出　　处：《西南师范大学学报（自然科学版）》2018年第4期31-36,共6页Journal of Southwest China Normal University(Natural Science Edition)

摘　　要：设M^n为等距浸入到伪黎曼空间形式N_p^(n+p)(c)中的完备类空子流形,平均曲率H有界且具有平行单位平均曲率向量场.如果M^n的平均曲率H满足相应条件,证明了该子流形的余维数p-可约化的问题.Let M n with parallel normalized mean curvature vector field be a complete spacelike submanifold isometric immersed into a semi-Riemannian space form N n+p p(c),whose mean curvature H is bounded.We prove that if the mean curvature H of M n satisfies the corresponding conditions,then the codimension of M n will be reduced.

关 键 词：类空子流形 伪黎曼空间形式 余维数约化 平均曲率 

分 类 号：O186.12[理学—数学]