Ricci ϕ-invariance on almost cosymplectic three-manifolds

Abstract

Abstract Let M 3 {M}^{3} be a strictly almost cosymplectic three-manifold whose Ricci operator is weakly ϕ \phi -invariant. In this article, it is proved that Ricci curvatures of M 3 {M}^{3} are invariant along the Reeb flow if and only if M 3 {M}^{3} is locally isometric to the Lie group E ( 1 , 1 ) E\left(1,1) of rigid motions of the Minkowski 2-space equipped with a left-invariant almost cosymplectic structure.