Lightlike Einstein hypersurfaces

In this thesis, Semi-Euclidean Spaces, Lightlike Hypersurfaces of Semi-Riemann Manifolds, Gauss-Codazzi Equations for Lightlike Hypersurfaces, Ricci Curvature, Homothetic Screen Lightlike Hypersurfaces, Einstein Manifolds and Einstein Hypersurfaces were studied. This thesis consists of four chapters. The rst chapter is the introduction.In the second chapter, basic de nitions and concepts used in the later chapter of the study are given. In addition, basic de nitions and theorems related to degenerate metrics, non-degenerate metrics, quasi orthonormal bases were examined. In the third chapter, the general de nitions and some known theorems of Lightlike Hypersurfaces of Semi-Riemann manifolds, Lightlike Transversal Vector Bundle of Lightlike Hypersurfaces, Induced Geometrical Objects on Lightlike Hypersurfaces and Gauss-Codazzi Equations for Lightlike Hypersurfaces are given. In the fourth and the last chapter, some theorems and concepts related to Ricci Curvature, Einstein Hypersurfaces, Einstein Screen Homothetic Lightlike Hypersurfaces are provided and results obtained with these concepts.