arXiv subjects

Dipen Ganguly

Publications and source records attributed to Dipen Ganguly.

5 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

Kenmotsu metric as conformal $η$-Ricci soliton

The object of the present paper is to characterize the class of Kenmotsu manifolds which admits conformal $η$-Ricci soliton. Here, we have investigated the nature of the conformal $η$-Ricci soliton within the framework of Kenmotsu manifolds. It is shown that an $η$-Einstein Kenmotsu manifold admitting conformal $η$-Ricci soliton is an Einstein one. Moving further, we have considered gradient conformal $η$-Ricci soliton on Kenmotsu manifold and established a relation between the potential vector field and the Reeb vector field. Next, it is proved that under certain condition, a conformal $η$-Ricci soliton on Kenmotu manifolds under generalized D-conformal deformation remains invariant. Finally, we have constructed an example for the existence of conformal $η$-Ricci soliton on Kenmotsu manifold.

math.DG↗

arXiv2021

On trans-Sasakian $3$-manifolds as $η$-Einstein solitons

The present paper is to deliberate the class of $3$-dimensional trans-Sasakian manifolds which admits $η$-Einstein solitons. We have studied $η$-Einstein solitons on $3$-dimensional trans-Sasakian manifolds where the Ricci tensors are Codazzi type and cyclic parallel. We have also discussed some curvature conditions admitting $η$-Einstein solitons on $3$-dimensional trans-Sasakian manifolds and the vector field is torse-forming. We have also shown an example of $3$-dimensional trans-Sasakian manifold with respect to $η$-Einstein soliton to verify our results.

math.DG↗

arXiv2021

Characteristics of almost conformal Ricci solitons on Sasakian manifold

In this paper, we characterize the potential function $f$ of the almost conformal gradient Ricci soliton on a Sasakian manifold in terms of the non-dynamical scalar field $p$ and deduce the necessary condition for the potential function $f$ to be constant. Furthermore, a relation between $λ$ and the potential function $f$ has been established. Finally, we prove a sufficient condition for an almost conformal Ricci soliton to be an almost conformal gradient Ricci soliton and also a characterization of the soliton in terms of shrinking, steady or expanding has been done.

math.DG↗

arXiv2021

Characteristics of conformal Ricci soliton on warped product spaces

Conformal Ricci solitons are self similar solutions of the conformal Ricci flow equation. This paper deals with the study of conformal Ricci solitons within the framework of warped product manifolds which extends the notion of usual Riemannian product manifolds. First, we prove that if a warped product manifold admits conformal Ricci soliton then the base and the fiber also share the same property. In the next section the characterization of conformal Ricci solitons on warped product manifolds in terms of Killing and conformal vector fields has been studied. Next, we prove that a warped product manifold admitting conformal Ricci soliton with concurrent potential vector field is Ricci flat. Finally, an application of conformal Ricci soliton on a class of warped product spacetimes namely, generalized Robertson-Walker spacetimes has been discussed.

math.DG↗