Certain Paracontact Metrics Satisfying the Critical Point Equation

Abstract

The aim of this paper is to study theCPE (Critical Point Equation) on some paracontact metric manifolds.First, we prove that if a para-Sasakian metric satisfies the CPE,then it is Einstein with constant scalar curvature -2n(2n+1). Next,we prove that if $(\kappa,\mu)$-paracontact metric satisfies theCPE, then it is locally isometric to the product of a flat$(n+1)$-dimensional manifold and $n$-dimensional manifold ofnegative constant curvature$-4$.