In this paper we consider contact metric R-harmonic manifolds M with ξ belonging to (κ, μ)-nullity distribution. In this context we have κ ≤ 1. If κ < 1, then M is either locally isometric to the product E × S(4), or locally isometric to E(2) (the group of the rigid motions of the Euclidean 2-space). If κ = 1, then M is an Einstein-Sasakian manifold. Mathematics Subject Classification: 53C05, 5...

In this paper we prove the existence of Einstein metrics, actually SasakianEinstein metrics, on nontrivial rational homology spheres in all odd dimensions greater than 3. It appears as though little is known about the existence of Einstein metrics on rational homology spheres, and the known ones are typically homogeneous. The are two exception known to the authors. Both involve Sasakian geometr...

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.