Abstract
The purpose of the present paper is to study Ricci solitons on Sasaki–Kenmotsu manifolds. It is shown that if the characteristic vector fields \(\xi\) and \(\psi\) are recurrent torse-forming vector fields on the Sasaki–Kenmotsu metric as a Ricci soliton, then both \(\xi\) and \(\psi\) are concurrent and Killing vector fields. We classify and characterize a Sasaki–Kenmotsu manifold admitting holomorphically planar conformal vector \((HPCV)\) field. Also, we prove that an \(HPCV\) field on a Sasaki–Kenmotsu manifold is solenoidal. Moreover, in a Sasaki–Kenmotsu manifold admitting \(HPCV\) field \(V\) with \(\phi V\neq 0\) , the \(HPCV\) field is the eigen vector of the Ricci operator with eigen value \(2n+1.\)
