Slant submanifolds of nearly Kaehlerian S^6

This study consists of 5 chapters. In the first chapter, we present some important researches about the structures studied in this thesis and introduce the subjects related to this thesis. The Second chapter consist of 6 sections. In the first section, we give the definitions of structures and examples supporting these definitions. In the Second section of the second chapter, we present Riemannian manifolds and the structures that are important for Riemannian manifolds. In the third section of the second chapter, we present Riemannian manifolds and the structures that are important for Riemannian manifolds. In the third section of the second chapter, we introduce submanifolds of Riemannian manifolds and express the Gauss, Codazzi, Ricci equations and the concept of a flat manifold. Then we introduce the concepts such as totally umbilical, totally geodesic and minimal submanifold and prove theorems involving them. In the fourth section of the second chapter, we first define almost complex manifolds with J structure and Nijenhius tensor and after that, we give the concept of almost Hermitian manifold. Subsequently, we give submanifolds of almost Hermitian manifolds and we study slant submanifolds in detail. Afterwards, we define nearly Kaehlerian manifolds and give some properties of its Nijenhius tensor. In the fifth part of the second chapter, we give the algebraic construction of the S6 sphere and we show that it is a nearly Kaehlerian manifold. We find the mean curvature of the nearly Kaehlerian S6 sphere and generalize some conclusions on it. In the last section of the second chapter we give conclusions about totally umbilical and totally geodesic submanifolds of the nearly Kaehlerian sphere. We use the results found in the previous section for studying these submanifolds. In the third chapter, we express the necessary materials and mathematical methods that are used for writing this thesis. The fourth chapter includes the findings of the thesis. In this chapter, we give some new results and original theorems on slant submanifolds of the nearly Kaehlerian S6 sphere. We give the condition when nearly Kaehlerian S6 sphere becomes a Kaehlerian slant submanifold and we give the curvature of totally umbilical proper slant submanifolds of nearly Kaehlerian S6 sphere. As a result, we show that a totally umbilical proper slant submanifold of S6 is an Einstein manifold. The fifth chapter includes the evaluation of the thesis.