Lorentz空间形式中类空超曲面的一个空隙定理

设M~n是(n+1)维Lorentz空间形式M_1~(n+1)(c)中无脐点类空超曲面.在M_1~(n+1)(c)的共形变换群下,M~n上的3个基本的共形不变量分别是:共形1-形式C,共形2-张量A,共形度量g.用κ表示共形法化数量曲率,?=A-1/ntr(A)g表示无迹共形2-张量,主要证明了一个空隙定理.

A Gap Theorem of Spacelike Hypersurfaces in Lorentzian Space Forms

Let M~n be a n-dimensional umbilic-free hypersurface in the(n + 1)-dimensional Lorentzian Space form M_1~(n+1)(c).Three basic invariants of M~n under the conformal transformation group of M_1~(n+1)(c)are a 1-form C,called conformal 1-form,a symmetric(0,2)tensor A,called conformal 2-tensor,and a positive definite(0,2)tensor g,called conformal metric.We denote the conformal normalized scalar curvature by κ and the trace-free conformal 2-tensor by ? =A-1/ntr(A)g.In this paper,we prove a gap theorem.