The Critical Point Equation on 3-dimensional α-cosymplectic Manifolds

Abstract

The object of the present paper is to study the critical point equation (CPE) on 3-dimensional α-cosymplectic manifolds. We prove that if a 3-dimensional connected αcosymplectic manifold satisfies the Miao-Tam critical point equation, then the manifold is of constant sectional curvature −α, provided Dλ 6= (ξλ)ξ. We also give several interesting corollaries of the main result.