A Class Of Spacelike Hypersurfaces In The Lorentz-Minkowski Space

In recent years, the study of spacelike hypersurfaces in the Lorentz-Minkowski space has been of increasing interest from both the physical and mathematical aspects. From a physical point of view, such interest is motivated by their role in the study of different problems in general relativity. From a mathematical point of view, spacelike hypersurfaces are also interesting by the fact that they exhibit nice Bernstein-type properties.Presently, the study of spacelike hypersurfaces in the Lorentz-Minkowski space has obtained great results, their interior structure and character is increasingly clear. In this paper, we deal with a class of spacelike hypersurfaces in the Lorentz-Minkowski space, they are similar to the Wulff shape in Euclidean space.Let Lⁿ⁺¹ denote the (n + 1)-dimensional Lorentz-Minkowski space, let Hⁿ denote the n-dimensional hyperbolic space.We consider the map:where gradF denotes the gradient of F on Hⁿ.We derive our main results for the spacelike hypersurface as an application of the moving-frame method and some obtained results on the Wulff shape.In the first chapter, we study the properties of the spacelike hypersurface and give a characterization of this kind of hypersurface by calculation.In the second chapter, we get an integral formula on the spacelike hypersurfaces from the divergence theorem, then we introduce an important operater T_r and generalizeit to higher order forms.