The present paper aims to deliberate the geometric composition of a perfect fluid spacetime with torse-forming vector field ? in connection conformal Ricci–Yamabe metric and ?-Ricci–Yamabe metric. We delineate conditions for soliton be expanding, steady or shrinking. also discuss on some special types such as dust fluid, dark radiation era. Furthermore, we design find its characteristics lastly...

This paper provides a study of some aspects of flat and curved BPS domain walls together with their Lorentz invariant vacua of four dimensional chiral N = 1 supergravity. The scalar manifold can be viewed as a one-parameter family of Kähler manifolds generated by a Kähler-Ricci flow equation. Consequently, a vacuum manifold characterized by (m,λ) where m and λ are the dimension and the index of...

We consider almost Riemann and Ricci solitons in a D-homothetically deformed Kenmotsu manifold having as potential vector field gradient field, solenoidal or the Reeb of structure, explicitly obtain scalar curvatures for some cases. also provide lower bound curvature initial when admits soliton.

On a complete non-compact gradient shrinking Ricci soliton, we prove the analyticity in time for smooth solutions of heat equation with quadratic exponential growth space variable. This condition is sharp. As an application, give necessary and sufficient on solvability backward class functions shrinkers.

Description of the research: Topological solitons are smooth, localised, finite energy solutions in non-linear field theories. The soliton number is conserved due to a topological constraint, such as a winding number or a non-trivial Chern class. Originally motivated from physics, these solitons give rise to interesting mathematical objects which can be studied using differential geometry and a...

We study some aspects of dyonic non-supersymmetric black holes of four dimensional N = 1 supergravity coupled to chiral and vector multiplets. The scalar manifold can be considered as a one-parameter family of Kähler manifolds generated by a Kähler-Ricci flow equation. This setup implies that we have a family of dyonic non-supersymmetric black holes deformed with respect to the flow parameter r...

In this paper, we extend the theory of Ricci flows satisfying a Type-I scalar curvature bound at finite-time singularity. [2], Bamler showed that rescaling procedure will produce singular shrinking gradient soliton with singularities codimension 4. We prove entropy conjugate heat kernel based time converges to soliton, and use characterize set flow solution in terms density function. This gener...

In this paper, we study conformal Ricci solitons and gradient on generalized ($\kappa,\mu$)-space forms. The conditions for the to be shrinking, steady, expanding are derived in terms of pressure p. We show under what a semi-symmetric form equipped with soliton forms an Einstein manifold.

Let $(g, X)$ be a K\"ahler-Ricci soliton on complex manifold $M$. We prove that if the K\"ahler $(M, g)$ can immersed into definite or indefinite space form of constant holomorphic sectional curvature $2c$, then $g$ is Einstein. Moreover, its Einstein rational multiple $c$.

In this paper, we have investigated some aspects of gradient $$\rho$$ -Einstein Ricci soliton in a complete Riemannian manifold. First, proved that the compact satisfying curvature conditions is isometric to Euclidean sphere by showing scalar becomes constant. Second, shown non-compact an integral condition, vanishes.