On almost Kenmotsu manifolds admitting conformal Ricci-Yamabe solitons

Jay Prakash Singh; C. Zosangzuala

doi:10.5269/bspm.63784

Jay Prakash Singh Mizoram University https://orcid.org/0000-0002-2050-3524
C. Zosangzuala Mizoram University https://orcid.org/0000-0003-4486-062X

Abstract

This paper aims to characterize almost Kenmotsu Manifolds admitting conformal Ricci-Yamabe solitons. First, we studied $(\kappa,\mu)'$ and generalized $(\kappa,\mu)'-$ almost Kenmotsu manifolds which admits conformal Ricci-Yamabe soliton. We have shown that a $(\kappa,\mu)'$ almost Kenmotsu manifold $M^{2n+1}$ admitting a conformal Ricci-Yamabe soliton is locally isometric to $\mathbb{H}^{n+1}(-4)\times\mathbb{R}^n$ provided $2\lambda-\beta\tau\neq4\alpha n\kappa-\left(p+\frac{2}{2n+1}\right)$. Also, we give conditions for the conformal pressure when the soliton is expanding, steady or shrinking. It is shown that if the manifold admits a conformal gradient Ricci-Yamabe soliton, then the potential vector field is a strict infinitesimal contact transformation. Finally, we construct an example of a $3-$dimensional almost Kenmotsu manifold satisfying conformal Ricci-Yamabe soliton.

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