Characteristics of almost conformal Ricci solitons on Sasakian manifold

TL;DR

This paper explores the properties and conditions of almost conformal Ricci solitons on Sasakian manifolds, focusing on the potential function, scalar field, and classification as shrinking, steady, or expanding.

Contribution

It characterizes the potential function in terms of scalar fields, establishes conditions for constancy, and relates the soliton type to the potential function on Sasakian manifolds.

Findings

Necessary condition for potential function to be constant.

Relation between $mbda$ and potential function $f$.

Characterization of soliton types: shrinking, steady, expanding.

Abstract

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 $\lambda$ 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.