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...

This article refers to:On characterizations of hypersurfaces in a Sasakian space forms with commuting operators

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...

In this paper we demonstrate the existence of Sasakian-Einstein structures on certain 2-connected rational homology 7-spheres. These appear to be the first non-regular examples of Sasakian-Einstein metrics on simply connected rational homology spheres. We also briefly describe the rational homology 7-spheres that admit regular positive Sasakian structures.

We study Ricci solitons in Lorentzian α-Sasakian manifolds. It is shown that a symmetric parallel second order covariant tensor in a Lorentzian α-Sasakian manifold is a constant multiple of the metric tensor. Using this it is shown that if LV g + 2S is parallel, V is a given vector field then (g, V ) is Ricci soliton. Further, by virtue of this result Ricci solitons for (2n + 1)-dimensional Lor...

We obtain sharp inequalities involving the Ricci curvature and scalar for anti-invariant Riemannian submersions from Sasakian space forms onto manifolds.