arXiv subjects

Sumanjit Sarkar

Publications and source records attributed to Sumanjit Sarkar.

4 recordsLinked to original sources

arXiv2025

Quasi-isometry between two almost contact metric manifolds

In this paper the notion of quasi-isometry between two Riemannian manifolds has been introduced. This idea is also imposed to study quasi-isometry between two almost contact metric manifolds. Moving further, some curvature properties of two quasi-isometrically embedded almost contact metric manifolds, $N(k)-$contact metric manifolds and Sasakian manifolds are investigated. Next, an illustrative example of a quasi-isometry between two Sasakian structures is constructed. Finally, a relation between the scalar curvature and the quasi-isometric constants for two quasi-isometric Riemannian manifolds has been established.

math.DG↗

arXiv2021

Geometry of para-Sasakian metric as an almost conformal $η$-Ricci soliton

In this paper, we initiate the study of conformal $η$-Ricci soliton and almost conformal $η$-Ricci soliton within the framework of para-Sasakian manifold. We prove that if para-Sasakian metric admits conformal $η$-Ricci soliton, then the manifold is $η$-Einstein and either the soliton vector field $V$ is Killing or it leaves $ϕ$ invariant. Here, we have shown the characteristics of the soliton vector field $V$ and scalar curvature when the manifold admitting conformal $η$-Ricci soliton and vector field is pointwise collinear with the characteristic vector field $ξ$. Next, we show that a para-Sasakian metric endowed an almost conformal $η$-Ricci soliton is $η$-Einstein metric if the soliton vector field $V$ is an infnitesimal contact transformation. We have also displayed that the manifold is Einstein if it represents a gradient almost conformal $η$-Ricci soliton. We have developed an example to display the alive of conformal $η$-Ricci soliton on 3-dimensional para-Sasakian manifold.

math.DG↗

arXiv2021

$*$-Conformal $η$-Ricci soliton within the framework of Kenmotsu manifolds

The goal of our present paper is to deliberate $*$-conformal $η$-Ricci soliton within the framework of Kenmotsu manifolds. Here we have shown that a Kenmotsu metric as a $*$-conformal $η$-Ricci soliton is Einstein metric if the soliton vector field is contact. Further, we have evolved the characterization of the Kenmotsu manifold or the nature of the potential vector field when the manifold satisfies gradient almost $*$-conformal $η$-Ricci soliton. Next, we have contrived $*$-conformal $η$-Ricci soliton admitting $(κ,μ)^\prime$-almost Kenmotsu manifold and proved that the manifold is Ricci flat and is locally isometric to $\mathbb{H}^{n+1}(-4)\times\mathbb{R}^n$. Finally we have constructed some examples to illustrate the existence of $*$-conformal $η$-Ricci soliton, gradient almost $*$-conformal $η$-Ricci soliton on Kenmotsu manifold and $(κ,μ)^\prime$-almost Kenmotsu manifolds.

math.DG↗

arXiv2021

Ricci solitons and certain related metrics on 3-dimensional trans-Sasakian manifold

In this paper we study certain types of metrics such as Ricci soliton, $*$-conformal Ricci soliton in 3-dimensional trans-Sasakian manifold. First we have shown that a 3-dimensional trans-Sasakian manifold of type $(α,β)$ admits a Ricci soliton where the covariant derivative of potential vector field in the direction of unit vector field $ξ$ is orthogonal to $ξ$. It is also shown that if the structure functions satisfy $α^2=β^2$ then the covariant derivative of the potential vector field in the direction of $ξ$ is a constant multiple of $ξ$. Further, we have evolved the nature of scalar curvature when the manifold satisfies $*$-conformal Ricci soliton of type $(α,β)$, provided $α\neq 0$. Finally, we present an example to verify our findings.

math.DG↗