Study of Sasakian manifolds admitting \(*\)-Ricci–Bourguignon solitons with Zamkovoy connection

Abstract

The present paper is designed to study the geometric composition of an n-dimensional Sasakian manifold with \(*\)-Ricci–Bourguignon soliton under Zamkovoy connection. Here, we have shown the characteristics of the soliton when it is satisfied by the metric of the Sasakian manifold with respect to Riemannian connection and also with respect to Zamkovoy connection. We have also acquired Laplace equation from the soliton equation when the potential vector field V of the soliton is of gradient type in terms of Zamkovoy connection. We have then studied some well known curvature tensor such as \(W_2\) curvature tensor and Q curvature tensor on the manifold when it admits the \(*\)-Ricci–Bourguignon soliton with respect to Zamkovoy connection.