The Evolutes Of Timelike Submanifolds In Anti De Sitter Space

The Lorentzian space form with the constant negative curvature is called Anti de Sitter space. We investigate the geometric meanings of the evolutes of timelike submanifolds with codimension one in Anti de Sitter space. We also study the contact between the timelike submanifolds and models as an application of Lagrangian singularity theory.There are three chapters in this paper. In chapter one, we prepare the basic definitions and notations in semi-Euclidean space with index 2. In chapter two, we investigate the geometric meanings of the evolutes of timelike curves in Anti de Sitter 2-space. We also consider the relationship between the contact of the timelike curves with the models and the singularities of the evolutes as an application of unfoldings theory.In chapter three, we study the evolutes of timelike hypersurfaces in Anti de Sitter n-space. Moreover, we investigate the contact of the timelike surfaces with families of models. Finally, we show some important results of the timelike surfaces in Anti de Sitter 3-space.