R1^m+1中拟迷向类空超曲面

Para-isotropic Spacelike Hypersurfaces in R1^m+1

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.