We have studied some geometric properties of conharmonically flat Sasakian manifold and an Einstein-Sasakian manifold satisfying R(X, Y ).N = 0. We have also obtained some results on special weakly Ricci symmetric Sasakian manifold and have shown that it is an Einstein manifold. AMS Mathematics Subject Classification (2000): 53C21, 53C25

We study canonical paracontact connection on a para-Sasakian manifold. We prove that a Ricci-flat para-Sasakian manifold with respect to canonical paracontact connection is an η-Einstein manifold.We also investigate some properties of curvature tensor, conformal curvature tensor,W2curvature tensor, concircular curvature tensor, projective curvature tensor, and pseudo-projective curvature tensor...

The object of this paper is to study $(epsilon)$-Lorentzian para-Sasakian manifolds. Some typical identities for the curvature tensor and the Ricci tensor of $(epsilon)$-Lorentzian para-Sasakian manifold are investigated. Further, we study globally $phi$-Ricci symmetric and weakly $phi$-Ricci symmetric $(epsilon)$-Lorentzian para-Sasakian manifolds and obtain interesting results.

In ([1]), T. Adati and K. Matsumoto defined para-Sasakian and special para-Sasakian manifolds which are considered as special cases of an almost paracontact manifold introduced by I. Sato and K. Matsumoto ([10]). In the same paper, the authors studied conformally symmetric para-Sasakian manifolds and they proved that an ndimensional (n>3) conformally symmetric para-Sasakian manifold is conforma...

We consider a nearly hyperbolic Sasakian manifold endowed with a quarter symmetric non-metric connection and study CRsubmanifolds of nearly hyperbolic Sasakian manifold endowed with a quarter symmetric nonmetric connection. We also obtain parallel distributions and discuss inerrability conditions of distributions on CR-submanifolds of nearly hyperbolic Sasakian manifold with quarter symmetric n...

In this paper, the geometry of invariant submanifolds of a Sasakian manifold are studied. Necessary and sufficient conditions are given on an submanifold of a Sasakian manifold to be invariant submanifold and the invariant case is considered. In this case, we investigate further properties of invariant submanifolds of a Sasakian manifold. M.S.C. 2000: 53C42, 53C15.

The object of the present paper is to study generalized -recurrent Sasakian manifolds. Here it is proved that a generalized -recurrent Sasakian manifold is an Einstein manifold. We also find a relation between the associated 1-forms A and B for a generalized -recurrent and generalized concircular -recurrent Sasakian manifolds. Finally, we proved that a three dimensional locally generalized -rec...

We study the Lie algebra of infinitesimal isometries on compact Sasakian and K–contact manifolds. On a Sasakian manifold which is not a space form or 3– Sasakian, every Killing vector field is an infinitesimal automorphism of the Sasakian structure. For a manifold with K–contact structure, we prove that there exists a Killing vector field of constant length which is not an infinitesimal automor...

In this paper, we have proved that a projectively flat Sasakian manifold is an Einstein manifold. Also, if an Einstein-Sasakian manifold is projectively flat, then it is locally isometric with a unit sphere S(1). It has also been proved that if in an Einsten-Sasakian manifold the relation K(X, Y ).P = 0 holds, then it is locally isometric with a unit sphere S(1). AMS Mathematics Subject Classif...

A transformation of an n-dimensional Riemannian manifold M , which transforms every geodesic circle of M into a geodesic circle, is called a concircular transformation. A concircular transformation is always a conformal transformation. Here geodesic circle means a curve in M whose first curvature is constant and second curvature is identically zero. Thus, the geometry of concircular transformat...