In this paper we study a new type of Riemannian manifold called generalized concircularly recurrent manifold. We obtain a necessary and sufficient condition for the constant scalar curvature of such a manifold. Next we study Ricci symmetric generalized concircularly recurrent manifold and prove that such a manifold is an Einstein manifold. Finally, we obtain a sufficient condition for a generalized concircularly recurrent manifold to be a special quasi-Einstein manifold.

The object of the present paper is to study a type of non-conformally flat semi-Riemannian manifolds called almost pseudo conformally symmetric manifold. The existence of an almost pseudo conformally symmetric manifold is also shown by a non-trivial example.

The object of the present paper is to study conformally flat almost pseudo Ricci symmetric manifolds. The existence of a conformally flat almost pseudo Ricci symmetric manifold with non-zero and non-constant scalar curvature is shown by a non-trivial example. We also show the existence of an n-dimensional non-conformally flat almost pseudo Ricci symmetric manifold with vanishing scalar curvature.

No abstract

The object of the present paper is to study pseudo Ricci symmetric manifolds. Among others we obtain a sufficient condition for a pseudo Ricci symmetric manifold to be a quasi Einstein manifold. We prove that in a pseudo Ricci symmetric quasi Einstein manifold the scalar curvature vanishes and pseudo Ricci symmetric quasi Einstein perfect fluid spacetime has also been considered. Also we construct two examples of pseudo Ricci symmetric manifolds to justify our theorems.