Lightlike Submanifolds of Semi-Riemann manifolds with quarter symmetric connection

This thesis consists of five chapters.The first chapter deals with the basic concepts of Riemann manifolds, product manifolds, lightlike hipersurface and submanifolds, quarter, semi-symmetric non-metric connections and complex submanifolds.Other chapters are the parts of original study. In the second chapter, lightlike hipersurface of a semi-Riemannian product manifold was investigated. Firstly ightlike hipersurfaces were classified, with the help of $F-$ product structure (screen semi-invariant, radical anti-invariant, screen invariant) and the results of this type of hipersurfaces were given. Later, the geometry of this type of lightlike hypersurfaces was considered with respect to quarter symmetric non-metric connection, which was obtained with the help of $F-$ product structure.In the third chapter, a new type of half-lightlike submanifolds (semi-invariant) was defined and first of all, these submanifolds were considered according to the Levi-Civita connection and induced connection. Subsecuently these submanifolds were investigated with respect to quarter symmetric non-metric connection.In the fourth chapter, some characteristics of coisotropic and $r-$ lightlike submanifolds of semi-Riemannian product manifold were evaluated with respect to Levi-Civita and quarter-symmetric non-metric connection.In the fifth chapter, semi-invariant lightlike submanifolds of indefinite Kaehler manifolds were examined with respect to Levi-Civita and quarter-symmetric non-metric connection.KEYWORDS: Quarter Symmetric Non-metric connection, Lightlike Hipersurface, Half-lightlike submanifold, Lightlike submanifold,Semi-Riemann product Manifold, Coisotropic submanifold, Screen invariant submanifold, Radical anti-invariant submanifold,Semi-invariant submanifold.