Ricci ϕ-invariance on almost cosymplectic three-manifolds

Abstract

Let M3{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 M3{M}^{3} are invariant along the Reeb flow if and only if M3{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.

Keywords

• almost cosymplectic three-manifolds
• ricci ϕ-invariance
• lie group
• 53d15
• 53c25