Geometry of almost contact metrics as almost $\ast$-Ricci solitons

Abstract

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

12 pages. arXiv admin note: text overlap with arXiv:2008.12497