The Geometry Of The Space-like Surface In The Semi-euclidean4-space With Index2

In this paper, we mainly research the local differential geometry nature of a space-likesurface in the semi-Euclidean4-space with index2. We established moving frame of thespace-like surface, then we obtain the second fundamental form of the space-like surface.Thus we can obtain a series of geometric invariants, such as the Gaussian curvature, the meancurvature, the quadric form and so on. So as to obtain a condition that the like-surface isdevelopable. In fact, they provide a theoretical basis which apply Legendrian singularitiestheory to give the classification of the singularities of the space-like surface.