Ximin Liu, Wenjie Wang: Locally ɸ-symmetric almost coKähler $3$-manifolds, 427-438

Abstract:

In this paper, we prove that an almost coKähler $3$-$h$-manifold is locally $\phi$-symmetric with scalar curvature invariant along the contact distribution if and only if it is locally isometric to the Euclidean $3$-space $\mathbb{R}^3$ or the Riemannian product $\mathbb{R}\times N^2(c)$, where $N^2(c)$ denotes a Kähler surface of constant curvature $c\neq0$, or the unimodular Lie group $E(1,1)$ of rigid motions of the Minkowski $2$-space equipped with a left invariant strictly almost coKähler structure.

Key Words: Almost coKähler 3-manifold, local $\phi$-symmetry, Lie group.

2010 Mathematics Subject Classification: Primary 53D15, 53C25.