Communications of the
Korean Mathematical Society CKMS

The main intention of the current paper is to characterize certain properties of $\star$-conformal Ricci solitons on non-coK\"ahler $(\kappa,\mu)$-almost coK\"{a}hler manifolds. At first, we find that there does not exist $\star$-conformal Ricci soliton if the potential vector field is the Reeb vector field $\theta$. We also prove that the non-coK\"ahler $(\kappa,\mu)$-almost coK\"ahler manifolds admit $\star$-conformal Ricci solitons if the potential vector field is the infinitesimal contact transformation. It is also studied that there does not exist $\star$-conformal gradient Ricci solitons on the said manifolds. An example has been constructed to verify the obtained results.

Keywords: Almost coK"{a}hler manifolds, $(kappa,mu)$-nullity distribution, infinitesimal contact transformation, $star$-Ricci tensors, Ricci solitons, conformal Ricci solitons

MSC numbers: Primary 53C15, 53D25