The Critical Point Equation on 3-dimensional α-cosymplectic Manifolds
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The object of the present paper is to study the critical point equation (CP E) 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 −α ^2 , provided Dλ 6= (ξλ)ξ. We also give several interesting corollaries of the main result.
Abstract
The object of the present paper is to study the critical point equation (CP E) 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 −α ^2 , provided Dλ 6= (ξλ)ξ. We also give several interesting corollaries of the main result.
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