Pseudosimetrik lightlike hiperyüzeyler

We study pseudosymmetric lightlike hypersurfaces of semi-Euclidean spaces and indefinite Sasakian space forms. After, we explain our motivation to study this problem and give related literatures, we give basic metarials used in the thesis. In the third chapter, we study pseudosymmetric lightlike hypersurfaces of semi- Euclidean spaces. We give an example, find sufficient conditions for a lightlike hypersurface to be pseudosymmetric and obtain characterizations of pseudosymmetric lightlike hypersurfaces of semi-Euclidean spaces. Then, we find sufficient conditions for a lightlike hypersurface to be pseudoparallel and give a characterization of pseudoparallel lightlike hypersurfaces. We also study Ricci-pseudosymmetric lightlike hypersurfaces, give an example and obtain characterizations for such lightlike hypersurfaces. In the fourth chapter, we study pseudosymmetric lightlike hypersurfaces of indefinite Sasakian space forms such that its sectional curvature c = 1. We first obtain integrability conditions for screen distribution of a lightlike hypersurface and then we find sufficient conditions for a lightlike hypersurface to be pseudosymmetric under integrable screen distribution. We also give a characterization of a pseudosymmetric lightlike hypersurface and investigate relations between pseudosymmetric lightlike hypersurface and its screen distribution. Moreover, we give sufficient conditions for a lightlike hypersurface of a Sasakian space form M(1) to be pseudoparallel, Ricci-pseudosymmetric and obtain characterizations for such hypersurfaces. In the last subsection, we check the e ect of Weyl projective pseudosymmetry conditions on the geometry of lightlike hypersurfaces.