On complete spacelike hypersurfaces with $R=aH+b$ in locally symmetric Lorentz spaces

Yingbo Han, Shuxiang Feng, and Liju Yu

Address:
College of Mathematics and Information Science, Xinyang Normal University, Xinyang 464000, Henan, P. R. China
College of Mathematics Physics and Information Engineering, Jiaxing University, Jiaxing 314001, Zhejiang, P. R. China

E-mail:
yingbhan@yahoo.com.cn
fsxhyb@yahoo.com.cn
yuliju96@163.com

Abstract: In this note, we investigate $n$-dimensional spacelike hypersurfaces $M^n$ with $R=aH+b$ in locally symmetric Lorentz space. Two rigidity theorems are obtained for these spacelike hypersurfaces.

AMSclassification: primary 53C42; secondary 53B30.

Keywords: spacelike submanifolds, locally symmetric Lorentz spaces.