We study Ricci solitons in Lorentzian α-Sasakian manifolds. It is shown that a symmetric parallel second order covariant tensor in a Lorentzian α-Sasakian manifold is a constant multiple of the metric tensor. Using this it is shown that if LV g + 2S is parallel, V is a given vector field then (g, V ) is Ricci soliton. Further, by virtue of this result Ricci solitons for (2n + 1)-dimensional Lor...

Abstract We study conformal $$\eta$$ ? -Einstein solitons on the framework of trans-Sasakian manifold in dimension three. Existence is discussed. Then we find some results which are where Ricci tensor cyclic parallel and Codazzi type. also consider curvature conditions with addition to manifold. use torse-for...

When Einstein was thinking about the theory of general relativity based on the elimination of especial relativity constraints (especially the geometric relationship of space and time), he understood the first limitation of especial relativity is ignoring changes over time. Because in especial relativity, only the curvature of the space was considered. Therefore, tensor calculations should be to...

We study the ∗-Ricci operator on Hopf real hypersurfaces in complex quadric. prove that for quadric, tensor is symmetric if and only unit normal vector field singular. In following, we obtain of quadric symmetric, then both Reeb-flow-invariant Reeb-parallel. As correspondence to semi-symmetric Ricci tensor, give a classification with tensor.

Let M^2n be a hoph hypersurfaces with parallel ricci operator and tangent to structure vector field in Sasakian space form. First, we show that structures and properties of hypersurfaces and hoph hypersurfaces in Sasakian space form. Then we study the structure of hypersurfaces and hoph hypersurfaces with a parallel ricci tensor structure and show that there are two cases. In the first case, th...

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.

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...

We describe all almost contact metric, almost hermitian and G 2-structures admitting a connection with totally skew-symmetric torsion tensor, and prove that there exists at most one such connection. We investigate its torsion form, its Ricci tensor, the Dirac operator and the ∇-parallel spinors. In particular, we obtain solutions of the type II string equations in dimension n = 5, 6 and 7.

We describe all almost contact metric, almost hermitian and G 2-structures admitting a connection with totally skew-symmetric torsion tensor, and prove that there exists at most one such connection. We investigate its torsion form, its Ricci tensor, the Dirac operator and the ∇-parallel spinors. In particular, we obtain solutions of the type II string equations in dimension n = 5, 6 and 7.