Compact space-like hypersurfaces with constant scalar curvature in locally symmetric Lorentz spaces

Yaning Wang and Ximin Liu

Department of Mathematics, South China University of Technology, Guangzhou 510641, GuangDong, P. R. China
School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, LiaoNing, P. R. China


Abstract: A new class of $(n+1)$-dimensional Lorentz spaces of index $1$ is introduced which satisfies some geometric conditions and can be regarded as a generalization of Lorentz space form. Then, the compact space-like hypersurface with constant scalar curvature of this spaces is investigated and a gap theorem for the hypersurface is obtained.

AMSclassification: primary 53C42; secondary 53C15.

Keywords: space-like hypersurface, constant scalar curvature, second fundamental form, locally symmetric Lorentz space.

DOI: 10.5817/AM2012-3-163