Spacetimes Admitting Concircular Curvaure Tensor in f(R) Gravity

The main object of this paper is to investigate spacetimes admitting concircular curvature tensor in f(R) gravity theory. At first, concircularly flat and concircularly flat perfect fluid spacetimes in fR gravity are studied. In this case, the forms of the isotropic pressure p and the energy density σ are obtained. Next, some energy conditions are considered. Finally, perfect fluid spacetimes with divergence free concircular curvature tensor in f(R) gravity are studied; amongst many results, it is proved that if the energy-momentum tensor of such spacetimes is recurrent or bi-recurrent, then the Ricci tensor is semi-symmetric and hence these spacetimes either represent inflation or their isotropic pressure and energy density are constants.

N(k)-contact metric manifolds with generalized Tanaka-Webster connection

In this paper, we characterize N(k)-contact metric manifolds with generalized Tanaka-Webster connection. We obtain some curvature properties. It is proven that if an N(k)-contact metric manifold with generalized Tanaka-Webster connection is K-contact then it is an example of generalized Sasakian space form. Also, we examine some flatness and symmetric conditions of concircular curvature tensor on an N(k)-contact metric manifolds with generalized Tanaka-Webster connection.

On a type of quarter-symmetric non-recurrent metric connection on a p-Sasakian manifold

We study a Para-Sasakian manifold admitting a type of quartersymmetric non-recurrent-metric connection whose concircular curvature tensor satisfies certain curvature conditions.

Geometry of concircular curvature tensor of Kahler manifolds

The study deals with the necessary condition where a nearly Kahler manifold of flat concircular tensor has been found. And the relationship between these invariants and additional properties of symmetry concircular tensor, as well as geometrical meaning of the reference in zero of these invariants . http://dx.doi.org/10.25130/tjps.25.2020.037

The Concircular Curvature Tensor Of The Locally Conformal Kahler Manifold

In this research, we are calculated components conharmonic curvature tensor in some aspects Hermeation manifolding in particular of the Locally Conformal Kahler manifold. And we prove that this tensor possesses the classical symmetry properties of the Riemannian curvature. They also, establish relationships between the components of the tensor in this manifold http://dx.doi.org/10.25130/tjps.24.2019.137

On concircular curvature tensor in a Lorentzian α-Sasakian manifold with respect to the quarter-symmetric non-metric connection

In the present paper, some properties of concircular curvature tensor in a Lorentzian α-Sasakian manifold with respect to the quarter-symmetric non-metric connection have been studied.