Korean J. Math.  Vol 29, No 2 (2021)  pp.445-453
DOI: https://doi.org/10.11568/kjm.2021.29.2.445

Para-Kenmotsu metric as a $\eta$-Ricci soliton

Satyabrota Kundu

Abstract


The purpose of the paper is to study of Para-Kenmotsu metric as a $\eta$-Ricci soliton. The paper is organized as follows:
* If an $\eta$-Einstein para-Kenmotsu metric represents an $\eta$-Ricci soliton with flow vector field $V$, then it is Einstein with constant scalar curvature $r = -2n(2n+1)$.
* If a para-Kenmotsu metric $g$ represents an $\eta$-Ricci soliton with the flow vector field $V$ being an infinitesimal paracontact transformation, then $V$ is strict and the manifold is an Einstein manifold with constant scalar curvature $r = -2n(2n+1)$.
* If a para-Kenmotsu metric $g$ represents an $\eta$-Ricci soliton with non-zero flow vector field $V$ being collinear with $\xi$, then the manifold is an Einstein manifold with constant scalar curvature $r = -2n(2n+1)$.
Finally, we cited few examples to illustrate the results obtained.


Keywords


Para-Kenmotsu, η-Ricci soliton, infinitesimal paracontact transformation, η-Einstein, Einstein.

Subject classification

53C15, 53C21, 53C25, 53D15.

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