Linear Weingarten Spacelike Hypersurfaces in Anti-de Sitter Space
袁小琴 1独力 1聂天1
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作者信息
1. 重庆理工大学理学院,重庆市 400054
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摘要
设Mn是Anti-de Sitter空间H1n+1(-1)中的n维紧致线性Weingarten类空超曲面,使得R=aH+b(a,b是常数),且(n-1)a2-4n(1+b)≥0,其中R和H分别是Mn的标准数量曲率和平均曲率.证明了如果Mn的第二基本形模长的平方 S 满足 S≤nH2+(B(H))2,或S≥nH2+(+H)2,或 n(R)≤S≤(n-1)n(R)+2/n-2+n-2/n(R)+2((R)=-1-R),那么Mn是全脐的,其中B(H)和B+H是多项式PH(x)=x2-n(n-2)√n(n-1)|H|x-n-nH2的两个实根.
Abstract
Let Mn be an n-dimensional compact linear Weingarten spacelike hypersurface in Anti-de Sitter space H1n+1(-1)with R=aH+b(a and b are constants)satisfying(n-1)a2-4n(1+b)≥0,where R and H are the normalized scalar curvature and the mean curvature of Mn.This paper proves that if the square of the length of the second fundamental form S of Mn satisfies S≤nH2+(B(H))2,or S≥nH2+(B+H)2,or(n(R)≤S≤(n-1)n(R)++2/n-2+n-2/n(R)+2((R)=-1-R)),then Mn is totally umbilical where B(H) and B+H are two real roots of the polynomial PH(x)=x2-n(n-2)/√n(n-1)|H|x-n-nH2.
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