h-Ricci soliton and Gradient h-Ricci soliton on para-Kenmotsu manifold

The current paper examines the h-Ricci soliton and gradient h-Ricci soliton on a para-Kenmotsu manifold when h has a definite signal. Firstly we show that h-Ricci soliton on the present manifold is Einstein whenever the potential vector field V is contact, and if the potential vector field V is collinear with the Reeb vector field ξ, then the manifold is n-Einstein manifold. Next, we prove that a η-Einstein para-Kenmotsu metric as an h-Ricci soliton reduces to Einstein manifold. Finally, we show that a similar result occurs in the case of gradient h-Ricci soliton.