Geometry of almost contact metrics as almost $*$-Ricci solitons

TL;DR

This paper characterizes almost $*$-Ricci solitons on Kenmotsu manifolds, showing conditions under which they are steady or Einstein, and explores geometric properties related to the Reeb vector field and potential vector fields.

Contribution

It provides new characterizations of almost $*$-Ricci solitons on Kenmotsu manifolds, including conditions for steadiness and Einstein metrics, based on geometric and vector field properties.

Findings

Steady $*$-Ricci soliton when potential vector field is Jacobi along Reeb vector field.

Kenmotsu manifold with an almost $*$-Ricci soliton is Einstein if $ ext{eta}$-Einstein or potential vector field is collinear with Reeb vector.

Conditions for the potential vector field being an infinitesimal contact transformation.

Abstract

In the present paper, we give some characterizations by considering $*$-Ricci soliton as a Kenmotsu metric. We prove that if a Kenmotsu manifold represents an almost $*$-Ricci soliton with the potential vector field $V$ is a Jacobi along the Reeb vector field, then it is a steady $*$-Ricci soliton. Next, we show that a Kenmotsu matric endowed an almost $*$-Ricci soliton is Einstein metric if it is $\eta$-Einstein or the potential vector field $V$ is collinear to the Reeb vector field or $V$ is an infinitesimal contact transformation.