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

Dhriti Sundar Patra; Akram Ali; Fatemah Mofarreh

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arXiv · 2101.01459

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

Dhriti Sundar Patra·Akram Ali·Fatemah Mofarreh

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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.

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Dhriti Sundar Patra, Akram Ali, Fatemah Mofarreh. 2021-01-05. Geometry of almost contact metrics as almost $*$-Ricci solitons. https://arxiv.org/abs/2101.01459

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