东南大学学报（英文版）2018，Vol.34Issue(2)：276-280,5.DOI:10.3969/j.issn.1003-7985.2018.02.018
局部对称Lorentz空间中线性Weingarten类空超曲面
Linear Weingarten spacelike hypersurface in locally symmetric Lorentz space
摘要
Abstract
The rigidity of spacelike hypersurface Mnimmersed in locally symmetric space Mn+1(1) is investigated, where the ( normalized) scalar curvature R and mean curvature H of Mn satisfy R = aH + b, and a, b are real constants. First, an estimate of the upper bound of the function L( nH) is given, where L is a second-order differential operator. Then, under the assumption that the square norm of the second fundamental form is bounded by a given positive constant, it is proved that Mnmust be either totally umbilical or contain two distinct principle curvatures, one of which is simple. Moreover, a similar result is obtained for complete noncompact spacelike hypersurfaces in locally symmetric Einstein spacetime. Hence, some known rigidity results for hypersurface with constant scalar curvature are extended for the linear Weingarten case.关键词
类空超曲面/线性Weingarten/局部对称Lorentz空间Key words
spacelike hypersurface/linear Weingarten/locally symmetric Lorentz space分类
数理科学引用本文复制引用
王佩君,潮小李,白苗苗..局部对称Lorentz空间中线性Weingarten类空超曲面[J].东南大学学报（英文版）,2018,34(2):276-280,5.基金项目
The Natural Science Foundation of Jiangsu Province ( No.BK20161412 ) , the Fundamental Research Funds for the Central Universities, the Scientific Innovation Research of College Graduates in Jiangsu Province ( No. KYCX17_0041) . （ No.BK20161412 ）
