In this paper, we consider $\left(LCS\right)_{n}$ manifold admitting almost $\eta-$Ricci solitons by means of curvature tensors. Ricci pseudosymmetry concepts soliton have introduced according to the choice some special tensors such as pseudo-projective, $W_{1}$, $W_{1}^{\ast}$ and $W_{2}.$ Then, again tensor, necessary conditions are searched for be semisymmetric. Then characterizations obtain...

In this paper, we consider Lorentz generalized Sasakian space forms admitting almost $\eta-$Ricci solitons in some curvature tensors. Ricci pseudosymmetry concepts of \ soliton have introduced according to the choice special tensors such as Riemann, concircular, projective, $\mathcal{M-}$projective, $W_{1}$ and $W_{2}.$ Then, again tensor, necessary conditions are given for form be semisymmetri...

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.

In this paper, we consider pseudosymmetric Lorentz Sasakian space forms admitting almost $\eta-$Ricci solitons in some curvature tensors. Ricci pseudosymmetry concepts of admits soliton have introduced according to the choice special tensors such as Riemann, concircular, projective, $\mathcal{M-}$projective, $W_{1}$ and $W_{2}.$ Then, again tensor, necessary conditions are given for form be sem...

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.