Korean J. Math. Vol. 28 No. 4 (2020) pp.847-863
DOI: https://doi.org/10.11568/kjm.2020.28.4.847

Certain solitons on generalized (κ,μ) contact metric manifolds

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Published: Dec 30, 2020
Keywords:
(κ,μ)-contact metric manifold, gradient Yamabe soliton, gradient Einstein soliton, closed m-quasi Einstein metric, conformal gradient Ricci soliton
Mathematics Subject Classification:
53C25, 53D15

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Avijit Sarkar
Department of Mathematics, University of Kalyani Kalyani-741235, West Bengal, India
Pradip Bhakta
Department of Mathematics, University of Kalyani Kalyani-741235, West Bengal, India

Abstract

The aim of the present paper is to study some solitons on three dimensional generalized (κ,μ)-contact metric manifolds. We study gradient Yamabe solitons on three dimensional generalized (κ,μ)-contact metric manifolds. It is proved that if the metric of a three dimensional generalized (κ,μ)-contact metric manifold is gradient Einstein soliton then μ=2κκ−2. It is shown that if the metric of a three dimensional generalized (κ,μ)-contact metric manifold is closed m-quasi Einstein metric then κ=λm+2 and μ=0. We also study conformal gradient Ricci solitons on three dimensional generalized (κ,μ)-contact metric manifolds.



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