Riv. Mat. Univ. Parma, Vol. 12, No. 2, 2021

Venkatesha Venkatesha [a], Huchchappa Aruna Kumara [a] and Devaraja Mallesha Naik [b]

On $$m$$-quasi Einstein almost Kenmotsu manifolds
Pages: 287-299
Accepted in revised form: 8 June 2021
Mathematics Subject Classification: 53C25, 53C15, 53D10.
Keywords: $$m$$-quasi Einstein metric, Ricci solitons, Kenmotsu manifolds, almost Kenmotsu $$(\kappa,\mu)'$$-manifolds, Einstein manifolds.
[a]: Department of Mathematics, Kuvempu University, Shankaraghatta, Karnataka 577-451, India.
[b]: Department of Mathematics, CHRIST (Deemed to be University), Bangalore (Bengaluru), Karnataka 560029, India.

V. Venkatesha and H.A. Kumara are thankful to Department of Science and Technology, New Delhi for financial assistance to the Department of Mathematics, Kuvempu University under the FIST program (Ref. No. SR/FST/MS-I/2018-23(C)).
Abstract: In this article, we consider $$m$$-quasi Einstein structures on two class of almost Kenmotsu manifolds. Firstly, we study a closed $$m$$-quasi Einstein metric on a Kenmotsu manifold. Next, we proved that if a Kenmotsu manifold $$M$$ admits an $$m$$-quasi Einstein metric with conformal vector field $$V$$, then $$M$$ is Einstein. Finally, we prove that a non-Kenmotsu almost Kenmotsu $$(\kappa,\mu)'$$-manifold admitting a closed $$m$$-quasi Einstein metric is locally isometric to the Riemannian product $$\mathbb{H}^{n+1}\times\mathbb{R}^n$$, provided that $$\frac{\lambda-\kappa(2n+m)}{2m}=1$$.

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