Conformal Ricci soliton and quasi-Yamabe soliton on generalized Sasakian space form

Abstract

The present paper is devoted to generalized Sasakian space forms admitting conformal Ricci soliton and Quasi-Yamabe soliton. Nature of the conformal Ricci soliton is characterized on generalized Sasakian space form with various types of the potential vector field, and conditions for the conformal Ricci soliton to be shrinking, steady, or expanding are also given. Then it is shown that, depending on the nature of the structure functions of a generalized Sasakian space form, the potential function of a conformal gradient Ricci soliton is constant. Next, it is proved that under certain conditions, a quasi-Yamabe soliton reduces to a Yamabe soliton on generalized Sasakian space forms. Finally, an illustrative example of a generalized Sasakian space form is discussed to verify our results.