Li̇ghtli̇ke altmani̇foldlar üzeri̇nde chen ti̇pi̇ eşi̇tsi̇zli̇kler

This study designed as a philosophy doctoral thesis covers five chapters. In the first chapter, the historical developments and the problems which are discussed in this thesis are presented. In the second chapter, basic definitions and theorems are explained and general facts about semi-Riemannian manifolds have been given. In the third chapter, some basic facts about lightlike hypersurfaces of a Lorentzian manifold are presented. Ricci curvature and scalar curvature for sub-plane section of these hypersurfaces are introduced. Various inequalities involving screen Ricci curvature and screen scalar curvature of screen homothetic lightlike hypersurfaces are established. By using these inequalities, some characterizations for lightlike hypersurfaces of a Lorentzian manifold are given. In the fourth chapter, firstly, some basic facts about half-lightlike submanifolds of a Lorentzian manifold are given. Ricci curvature and scalar curvature for sub-plane section of such manifold are introduced and some inequalities involving screen Ricci curvature and screen scalar curvature of screen homothetic half-lightlike submanifolds are established. Also, equality case of these inequalities are investigated. In the fifth chapter, some basic information about coisotropic lightlike submanifolds of a semi-Riemannian manifold with index two is mentioned. Screen Ricci curvature and screen scalar curvature of these submanifolds are introduced. Some inequalities involving these curvatures are established. These inequalities are investigated on submanifolds of semi-Euclidean space with index two.