A study of critical point equation and *-critical point equation on Sasakian manifolds

Abstract

In this paper, we initiate the study of critical point equation and *-critical point equation within the substructure of Sasakian manifolds. We prove that if a compact Sasakian manifold admits CPE, then either the manifold is Einstein or the potential function is harmonic in an open subset. Later, we demonstrate that if the manifold satisfies *-CPE, it is [Formula: see text]-Einstein and obtain an expression for the *-Ricci tensor. Finally, we construct an example to illustrate the existence of CPE and *-CPE on the Sasakian manifold.