Let s ≥ 2. We construct Ricci flat pseudo-Riemannian manifolds of signature (2s, s) which are not locally homogeneous but whose curvature tensors never the less exhibit a number of important symmetry properties. They are curvature homogeneous; their curvature tensor is modeled on that of a local symmetric space. They are spacelike Jordan Osserman with a Jacobi operator which is nilpotent of ord...

The object of the present paper is to characterize Cotton tensor on a 3-dimensional Sasakian manifold admitting $\eta$-Ricci solitons. After introduction, we study manifolds and introduce new notion, namely, pseudo-symmetric manifolds. Next deal with 3-manifold Among others prove that such constant scalar curvature Einstein some appropriate conditions. Also, classify nature soliton metric. Fina...

The study of weakly symmetric and weakly projective symmetric manifold were initiated by Tamassy and Binh in 1989. Later on several authors studied weakly symmetric Riemannian manifold and analogous structures, viz. Weakly Ricci symmetric, weakly projective symmetric and weakly conformally symmetric Riemannian manifolds. At first we cited examples of weakly symmetric Riemannian manifolds. Next ...

Commutative properties of four-dimensional generalized symmetric pseudo-Riemannian manifolds were considered. Specially, in this paper, we studied Skew-Tsankov and Jacobi-Tsankov conditions in 4-dimensional pseudo-Riemannian generalized symmetric manifolds.

The object of the present paper is to characterize pseudo Ricci symmetric twisted spacetimes. At first it shown that a spacetime GRW spacetime. Next, we obtain necessary and sufficient condition for be perfect fluid It also proved fluid, provided conformal curvature tensor divergence free. Moreover, investigate shear vorticity vector fields such type spacetimes pointed out its implications towa...

In this paper we introduce the concept of (ε)-almost paracontact manifolds, and in particular, of (ε)-para Sasakian manifolds. Several examples are presented. Some typical identities for curvature tensor and Ricci tensor of (ε)-para Sasakian manifolds are obtained. We prove that if a semi-Riemannian manifold is one of flat, proper recurrent or proper Ricci-recurrent, then it can not admit an (ε...

in the first part of this paper, some theorems are given for a riemannian manifold with semi-symmetric metric connection. in the second part of it, some special vector fields, for example, torse-forming vector fields, recurrent vector fields and concurrent vector fields are examined in this manifold. we obtain some properties of this manifold having the vectors mentioned above.

Theories of gravity are fundamentally a relation between matter and the geometric structure underlying spacetime. So once we put some additional restrictions on spacetime geometry, theory is bound to get impact, irrespective whether it general relativity or modified theories gravity. In present article, consider two curvature-based constraints, namely almost pseudo-Ricci symmetric weakly Ricci ...

In the paper we consider almost geodesic mappings of first type spaces with affine connections onto generalized 2-Ricci-symmetric spaces, 3-Ricci-symmetric and m-Ricci-symmetric spaces. either case main equations for are obtained as a closed system linear differential Cauchy in covariant derivatives. The results extend an amount research produced by N.S. Sinyukov, V.E. Berezovski, J. Mikeš.

In earlier work, carrying out numerical simulations of the Ricci flows of families of rotationally symmetric geometries on S3, we have found strong support for the contention that (at least in the rotationally symmetric case) the Ricci flow for a “critical” initial geometry– one which is at the transition point between initial geometries (on S3) whose volume-normalized Ricci flows develop a sin...