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 $(\kappa, \mu)$ contact metric manifolds

Avijit Sarkar, Pradip Bhakta

Abstract


The aim of the present paper is to study some solitons on three dimensional generalized $(\kappa, \mu)$-contact metric manifolds. We study  gradient Yamabe solitons on three dimensional generalized $(\kappa, \mu)$-contact metric manifolds. It is proved that if the metric of a three dimensional generalized $(\kappa, \mu)$-contact metric manifold is gradient Einstein soliton then $\mu = \frac{2\kappa}{\kappa - 2}.$ It is shown that if the metric of a three dimensional generalized $(\kappa, \mu)$-contact metric manifold is closed m-quasi Einstein metric then $\kappa = \frac{\lambda}{m + 2}$ and $\mu = 0.$ We also study conformal gradient Ricci solitons on three dimensional generalized $(\kappa, \mu)$-contact metric manifolds.


Keywords


$(\kappa, \mu)$-contact metric manifold, gradient Yamabe soliton, gradient Einstein soliton, closed $m$-quasi Einstein metric, conformal gradient Ricci soliton

Subject classification

53C25, 53D15

Sponsor(s)



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