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

## 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.

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