The purpose of this article is to study implications a Ricci soliton warped product manifold its base and fiber manifolds. First, it proved that if then factors are soliton. Then we on manifolds admitting either conformal vector field or concurrent field. Finally, some space-times.

In this note, we prove triviality and nonexistence results for gradient Ricci soliton warped metrics. The proofs stem from the construction of solitons that are realized as products, which know base spaces these products Ricci-Hessian type manifolds. We study latter class manifolds most appropriate setting to our results.

Abstract In this paper, we study $$\eta$$ ? -Ricci solitons on almost cosymplectic $$(k,\mu )$$ ( k , ? ) -manifolds. As an application, it is proved that if -metric with $$k&lt;0$$ &lt;</mml:mo...

The object of the present paper is to characterize class Kenmotsu manifolds which admits conformal $$\eta $$ -Ricci soliton. Here, we have investigated nature soliton within framework manifolds. It shown that an -Einstein manifold admitting Einstein one. Moving further, considered gradient on and established a relation between potential vector field Reeb field. Next, it proved under certain con...

In this paper we address several aspects of flat Bogomolnyi-PrasadSommerfeld (BPS) domain walls together with their Lorentz invariant vacua of 4d N = 1 supergravity coupled to a chiral multiplet. The scalar field spans a one-parameter family of 2d Kähler manifolds satisfying a Kähler-Ricci flow equation. We find that BPS equations and the scalar potential deform with respect to the real paramet...

In this paper we address several aspects of flat Bogomolnyi-PrasadSommerfeld (BPS) domain walls together with their Lorentz invariant vacua of 4d N = 1 supergravity coupled to a chiral multiplet. The scalar field spans a one-parameter family of 2d Kähler manifolds satisfying a Kähler-Ricci flow equation. We find that BPS equations and the scalar potential deform with respect to the real paramet...

Perelman [Pe02] has discovered a remarkable variational structure for the Ricci flow: it can be viewed as the gradient flow of the entropy functional λ. There are also two monotonicity formulas of shrinking or localizing type: the shrinking entropy ν, and the reduced volume. Either of these can be seen as the analogue of Huisken’s monotonicity formula for mean curvature flow [Hu90]. In various ...

We indicate some formulas connecting Ricci flow and Perelman entropy to Fisher information, differential entropy, and the quantum potential. 1. FORMULAS INVOLVING RICCI FLOW Certain aspects of Perelman’s work on the Poincaré conjecture have applications in physics and we want to suggest a few formulas in this direction; a fuller exposition will appear in a longer paper [11] and in a book in pre...