R1^m+1中拟迷向类空超曲面  

Para-isotropic Spacelike Hypersurfaces in R1^m+1

作　　者：姬秀 李同柱 Xiu JI;Tong Zhu LI(Department of Mathematics,Beijing Institute of Technology,Beijing 100081,P.R.China)

机构地区：[1]北京理工大学数学与统计学院,北京100081

出　　处：《数学学报（中文版）》2021年第1期47-58,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11571037)。

摘　　要：设f:M^m→R1^m+1是无脐点类空超曲面,则在Mm上可以定义四个基本的共形不变量:共形度量g,共形1-形式C,共形第二基本形式B,共形Blaschke张量A.如果存在光滑函数λ和常数μ,使得A+μB=Ag,则称M^m是拟迷向类空超曲面.本文不仅构造了拟迷向类空超曲面的例子,同时在相差R1^m+1的一个共形变换下,本文还完全分类了拟迷向类空超曲面.Let f:M^m→ R1^m+1 be an umbilic-free spacelike hypersurface.Four basic conformal invariants of Mm are the conformal metric g,the conformal 1-form C,the conformal second fundamental form B,and the conformal Blaschke tensor A.M^m is called the para-isotropic spacelike hypersurface,if A+μB=λg for some constant μand smooth function λ.We not only constructed examples which are para-isotropic spacelike hypersurfaces but also classified completely all para-isotropic spacelike hypersurfaces under the conformal transformal group of R1^m+1in this paper.

关 键 词：共形度量 共形第二基本形式 共形拟Blaschke张量 

分 类 号：O186.1[理学—基础数学]