A considerable interest has been shown to the study of physical properties of spacetimes which are conformal to certain well known gravitational fields. The general theory of relativity is believed by a number of unknown functions the ten components of g . Hence there is a little hope of finding physically interesting results without making reduction in their number. In conformally flat spaceti...

The aim of the present paper is to study properties of Quasi conformally flat LP-Sasakian manifolds with a coefficient α. In this paper, we prove that a Quasi conformally flat LP-Sasakian manifold M (n > 3) with a constant coefficient α is an η−Einstein and in a quasi conformally flat LP-Sasakian manifold M (n > 3) with a constant coefficient α if the scalar curvature tensor is constant then M ...

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 discuss expansions for the Cotton-York tensor near infinity for arbitrary slices of stationary spacetimes. From these expansions it follows directly that a necessary condition for the existence of conformally flat slices in stationary solutions is the vanishing of a certain quantity of quadrupolar nature (obstruction). The obstruction is nonzero for the Kerr solution. Thus, the Kerr metric a...

Our goal in this paper is to obtain further information about the curvature of gradient shrinking Ricci solitons. This is important for a better understanding and ultimately for the classification of these manifolds. The classification of gradient shrinkers is known in dimensions 2 and 3, and assuming locally conformally flatness, in all dimensions n ≥ 4 (see [14, 13, 6, 15, 20, 12, 2]). Many o...