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

preprint2021arXivOpen access

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 VV 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 ηη-Einstein or the potential vector field VV is collinear to the Reeb vector field or VV is an infinitesimal contact transformation.

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