Trans-sasakian manifolds

The aim of this thesis is to study some curvature conditions on Trans-Sasakian manifolds. The thesis has three chapters. First chapter contains some fundamental definitions and results which will be used in other chapters. Second chapter contains some fundamental definitions,theorems and results about Sasakian and Trans-Sasakian manıfolds. Chapter three contains original works. In the first chapter the we introduce basic definitions such as, Riemannian curvature tensor, Einstein manifold, Weyl Conformal curvature tensor, projective curvature tensor and almost contact metric manifolds. In the second chapter the definitions of Sasakian manifold, Sasakian space form, Trans- Sasakian manifold and teh basic theorems and propositions which are connected with these definitions have been given. In the last chapter some curvature conditions and equations which are used to provide these curvature conditions about Riemann curvature tensor, projective curvature tensor, Weylconformal curvature tensor on Trans-Sasakian manifolds are given. Under the light of these given information, the written theorems have been proved and results have been obtained. Keywords: Almost contact metric manifold, Einstein manifold, Riemannian curvature tensor, Sasakian Manifold, Trans-Sasakian manifold, Weyl-conformal curvature tensor.