Generalized Φ-Recurrent Sasakian Manifolds

This thesis consists of four chapters. The first chapter has been devoted to the introduction. In the second chapter, contact manifolds and Sasakian manifolds which are necessary for this study are introduced. In the third section, the notion of recurrent Sasakian manifolds which generalizes the Notion of locally symmetric Sasakian manifolds are introduced. recurrent Sasakian manifolds are studied and showed that such a manifold is always an Einstein manifold. It is proved that in a recurrent Sasakian manifold, the characteristic vector field and the vector field, p associated to the 1-form A are codirectional. It is showed that recurrent Sasakian manifold with non-zero constant sectional curvature reduces to a locally symmetric manifold. In the fourth section, the Notion of generalized recurrent Sasakian manifold is introduced and its various geometric properties with the existence of such Notion are studied. Generalized concircularly recurrent Sasakian manifolds are introduced. Finally süper generalized Ricci-recurrent manifold is introduced and it is showed that generalized concircularly recurrent Sasakian manifold M, n≥3 is süper generalized Ricci recurrent manifold. It is obtained that in a generalized concircularly recurrent Sasakian manifold M, n≥3, the vector field p2 associated with the 1-form B and the characteristic vector field are codirectional. Keywords: Einstein Manifold, Generalized Recurrent Sasakian Manifold, Sectional Curvature, Locally Symmetric Sasakian Manifold, Recurrent Sasakian Manifold, Scalar Curvature.