Bulletin of the
Korean Mathematical Society BKMS

We investigate the spacelike hypersurface $M^n$ with constant mean curvature (CMC) in a Lorentz Einstein manifold $L^{n+1}_1$, which is supposed to obey some appropriate curvature constraints. Applying a suitable Simons type formula jointly with the well known generalized maximum principle of Omori-Yau, we obtain some rigidity classification theorems and pinching theorems of hypersurfaces.

Keywords: Lorentz Einstein manifold, rigidity theorem, spacelike hypersurface

MSC numbers: Primary 53C20, 53B30, 53C42

Supported by: This work was supported by the National Natural Science Foundation of China (Grant Nos.\,11761061, 11261051).