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 α-cosymplectic manifold satisfies the Miao-Tam critical point equation, then the manifold is of constant sectional curvature −α², provided Dλ ≠ (ξλ)ξ. We also give several interesting corollaries of the main result.

Keywords: critical point equation, 3-dimensional α-cosymplectic manifolds