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Conformal $η$ $η$ -Ricci almost solitons of Kenmotsu manifolds

Santu Dey

https://orcid.org/0000-0002-2601-3788

Department of Mathematics, Bidhan Chandra College, Asansol 713304, India

E-mail Address: santu.mathju@gmail.com

Corresponding author.

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and

Siraj Uddin

Department of Mathematics, Faculty of Science, King Abdulaziz University, 21589 Jeddah, Saudi Arabia

E-mail Address: siraj.ch@gmail.com

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https://doi.org/10.1142/S0219887822501213Cited by:18 (Source: Crossref)

Abstract

The aim of this paper is to find some important classes of Einstein manifolds using conformal $η$ $η$ -Ricci solitons and conformal $η$ $η$ -Ricci almost solitons. We prove that a Kenmotsu metric as conformal $η$ $η$ -Ricci soliton is Einstein if it is $η$ $η$ -Einstein or the potential vector field $V$ $V$ is infinitesimal contact transformation or collinear with the Reeb vector field $ξ$ $ξ$ . Next, we prove that a Kenmotsu metric as gradient conformal $η$ $η$ -Ricci almost soliton is Einstein if the Reeb vector field leaves the scalar curvature invariants. Finally, we construct some examples to illustrate the existence of conformal $η$ $η$ -Ricci soliton, gradient almost conformal $η$ $η$ -Ricci soliton on Kenmotsu manifold.

Keywords:

AMSC: 53C15, 53C25, 53D15

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