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

Document Type : Original Article

Authors

Mohammad Amin Sedghi

Hajar Ghahremani-Gol

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

10.22034/kjm.2020.243367.1960

Abstract

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.

Keywords

Critical point equations

Cosymplectic manifold

Scalar curvature

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