We show that every K-contact Einstein manifold is Sasakian-Einstein and discuss several corollaries of this result.

The object of the present paper is to study three-dimensional Lorentzian -Sasakian manifolds which are Ricci-semisymmetry, locally symmetric and have -parallel Ricci tensor. An example of a three-dimensional Lorentzian -Sasakian manifold is given which verifies all the Theorems.

We prove that the dimension of the 1-nullity distributionN(1) on a closed Sasakianmanifold M of rank l is at least equal to 2l−1 provided thatM has an isolated closed characteristic. The result is then used to provide some examples ofK-contact manifolds which are not Sasakian. On a closed, 2n+ 1-dimensional Sasakian manifold of positive bisectional curvature, we show that either the dimension o...

In this paper, we study the geometry of lightlike hypersurfaces of an indefinite trans-Sasakian manifold with a quarter-symmetric metric connection. The main result is a characterization theorem for such a lightlike hypersurface of an indefinite generalized Sasakian space form. Mathematics Subject Classification: 53C25, 53C40, 53C50

Sasakian manifolds provide rich source of constructing new Einstein manifolds in odd dimensions [2]. They play some important role in the superstring theory in mathematical physics [19, 20]. There is a renewed interest on Sasakian manifolds recently. The present paper is devoted to the regularity analysis of a geodesic equation in the space of Sasakian metrics H (definition in (1.2)) and some o...

We show that every K-contact Einstein manifold is Sasakian-Einstein and discuss several corollaries of this result.

We discuss the Sasakian geometry of odd dimensional homotopy spheres. In particular, we give a completely new proof of the existence of metrics of positive Ricci curvature on exotic spheres that can be realized as the boundary of a parallelizable manifold. Furthermore, it is shown that on such homotopy spheres Σ the moduli space of Sasakian structures has infinitely many positive components det...

We show that every K-contact Einstein manifold is Sasakian-Einstein and discuss several corollaries of this result.