Lorentz空间型中具有调和曲率张量的类空超曲面

Space-Like Hypersurfaces with Harmonic Curvature Tensor in the Lotrntz Space

Mn为Lorentz空间型Nn1+1(c)中具有调和黎曼曲率的紧致类空超曲面,且Mn的平均曲率为常数,给出了这类超曲面的分类,如果Mn是极大的,也给出了反de Sitter空间中这类超曲面的一个刚性定理.

Let M^n be compact space-like hypersurfaces with harmonic Riemannian curvature tensor in theLorentz space N1＋1^n＋1 （c）. If the mean curvature of M^n is constant, we give the classification of the space-like hypersurfaces. In addition, if M^n is maximal, we obtain a rigidity theorem of the space-like hypersurfaces in the anti-de Sitter space in this paper.