Some curvature conditions on Para sasakian manifolds

SOME CURVATURE CONDITIONS ON PARA SASAK AN MAN FOLDSMehmet Alattin DEM RLDepartment of MathematicsMSc. Thesis 2007Supervisor: Asist.Prof.Dr. Ahmet YILDIZABSTRACTThe aim of this thesis is to study some curvature conditions on Para-Sasakianmanifolds. The thesis has three chapters.First chapter contains some fundamental definitions and results which will be used inother chapters. Second chapter contains some fundamental definitions, theorems and resultsabout Sasakian and Para-Sasakian manifolds. Chapter three contains original works.In the first chapter we introduce basic definitions such as, Riemannian curvature tensor,Einstein manifold, Weyl Conformal curvature tensor, projective curvature tensor,Conhormonical curvature tensor and almost contact metric manifolds.In the second chapter the definitions of Sasakian manifold, sasakian space form, Para-Sasakian manifold and the basic theorems and propositions which are connected with thesedefinitions have been given.In the last chapter some curvature conditions and equations which are used to providethese curvature conditions about Riemann curvature tensor, conharmonical curvature tesor,Weyl-conformal curvature tensor on Para-Sasakian manifolds are given. Under the light of thesegiven information, the written theorems have been proved and results have been obtained.Keywords: Riemannian curvature tensor, Einstein manifold, η - Einstein manifold,Weyl-conformal tensor, almost contact metric manifold, Para-Sasakian manifold