A note on critical point equations on three-dimensional cosymplectic manifolds

Document Type : Original Article


Department of Mathematics, Faculty of Science, Shahed University,Tehran, Iran



The goal of this note is to investigate some properties of the critical point equations on the $3$-dimensional $f$- cosymplectic manifolds. We obtain some geometric equations on the $3$-dimensional $f$-cosymplectic manifolds which admit critical point equations. We give a relation between $f$ and $\tilde{f}$ for a CPE metric on the three dimensional $f$-cosymplectic manifold to be Einstein. Also we obtain an eigenvalue of the Laplace operator on the $3$-dimensional $f$-cosymplectic manifolds with CPE metrics.