In this paper, we consider Lorentzian para-Kenmotsu manifold admitting almost $\eta-$Ricci solitons by virtue of some curvature tensors. Ricci pseudosymmetry concepts manifolds soliton have introduced according to the choice tensors such as Riemann, concircular, projective, $\mathcal{M-}$projective, $W_{1}$ and $W_{2}.$ After then, tensors, necessary conditions are given for be semisymmetric. T...

In this paper, we initiate the study of conformal $\eta$-Ricci soliton and almost within framework para-Sasakian manifold. We prove that if metric admits soliton, then manifold is $\eta$-Einstein either vector field $V$ Killing or it leaves $\phi$ invariant. Here, have shown characteristics scalar curvature when admitting pointwise collinear with characteristic $\xi$. Next, show a endowed an in...

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...

Ricci solitons (RS) have an extensive background in modern physics and are extensively used cosmology general relativity. The focus of this work is to investigate almost (RAS) on Lorentzian manifolds with a special metric connection called semi-symmetric u-connection (SSM-connection). First, we show that any quasi-Einstein manifold having SSM-connection, whose RS, Einstein manifold. A similar c...

We give the necessary and sufficient conditions for a gradient Ricci-Yamabe soliton with warped product metric. As physical applications, we consider solitons on generalized Robertson-Walker space-times standard static space-times.

In this note we provide a direct proof of the following: Any compact KRS with positive bisectional curvature is CP. As a corollary, we obtain an alternative proof of the Frankel conjecture by using the Kähler-Ricci flow. The purpose of this note is to give a proof of the following theorem, which does not rely on the solution of the Frankel conjecture: Theorem 1. Every compact complex manifold a...