Semi-symmetric hypersurfaces

This master thesis consists of four chapters. The first chapter, is the introduction. In the second chapter, basic definitions and concepts of semi- Riemann manifolds, vektor bundls, degenerate metrics, quasi orthonormal bases which will be useful for other depertments, are discussed. In the third chapter, Lightlike hypersurface of semi-Riemann manifolds have been introduced and theorems about lightlike hypersurface have been given. In addition, the general definitions and some theorems of transversal vektor bundle lightlike hypersurfaces, Induced geometrical objects on lightlike hypersurfaces and guass-codazzi equations for lightlike hypersurfaces are given. In the fourth chapter, we investigate lightlike hypersurfaces which are semi- symmetric, Ricci semi-symmetric, semi-parallel in a semi-Eucliean space. We obtain that every screen conformal lihtlike hypersurface of the Minkowski spacetime is semi-symmetric. Besides we investigate the semi-symmetric condition of a screen conformal lightlike hypersurface reduces to the semi-symmetric condition of a leaf of its screen distribution. Finally we obtain that semi-symmetric and Ricci semi-symmetric lightlike hypersurface are totally geodesic under certain conditions. Moreover we showed that there exist no non-totally geodesic parallel hypersurfaces a lorentzian space.