A New Class of Almost Ricci Solitons and Their Physical Interpretation

Abstract

We establish a link between a connection symmetry, called conformal collineation, and almost Ricci soliton (in particular Ricci soliton) in reducible Ricci symmetric semi-Riemannian manifolds. As a physical application, by investigating the kinematic and dynamic properties of almost Ricci soliton manifolds, we present a physical model of imperfect fluid spacetimes. This model gives a general relation between the physical quantities (u, μ, p, α, η, σ ij) of the matter tensor of the field equations and does not provide any exact solution. Therefore, we propose further study on finding exact solutions of our viscous fluid physical model for which it is required that the fluid velocity vector u be tilted. We also suggest two open problems.

Remarks on Some Soliton Types with Certain Vector Fields

“…Here, £ stands for the Lie derivative and Ω is a function on the manifold [10]. For more details related to symmetry inheritance applications on manifolds, please see ( [9,10,13,28]).…”

Professor Krishan L. Duggal: A Biographical Note

“…Subsequently, this approach on lightlike submanifolds attracted the attention of several geometers. His last two projects were (1) Ricci almost solitons and physical applications [5], and (ii) Contact pseudo Framed manifolds with applications [6].…”

Four‐dimensional gradient almost Ricci solitons with harmonic Weyl curvature

“…We also note that some physical interpretation of semi‐Riemannian almost Ricci solitons was given as imperfect fluid spacetimes in [14] and that almost Ricci solitons were generalized to h ‐almost Ricci soltons in [15].…”