Critical point equation on almost f-cosymplectic manifolds

Abstract

Purpose – Besse first conjectured that the solution of the critical point equation (CPE) must be Einstein. The CPE conjecture on some other types of Riemannian manifolds, for instance, odd-dimensional Riemannian manifolds has considered by many geometers. Hence, it deserves special attention to consider the CPE on a certain class of almost contact metric manifolds. In this direction, the authors considered CPE on almost f-cosymplectic manifolds. Design/methodology/approach – The paper opted the tensor calculus on manifolds to find the solution of the CPE. Findings – In this paper, in particular, the authors obtained that a connected f-cosymplectic manifold satisfying CPE with \lambda=\tilde{f} is Einstein. Next, the authors find that a three dimensional almost f-cosymplectic manifold satisfying the CPE is either Einstein or its scalar curvature vanishes identically if its Ricci tensor is pseudo anti‐commuting. Originality/value – The paper proved that the CPE conjecture is true for almost f-cosymplectic manifolds.

Keywords

• Critical point equation
• Almost f-cosymplectic manifold
• Cosymplectic manifold
• Einstein manifold