Cotton tensors on almost coKähler 3-manifolds
Volume 120 / 2017
Annales Polonici Mathematici 120 (2017), 135-148
MSC: Primary 53D15; Secondary 53C25.
DOI: 10.4064/ap170410-3-10
Published online: 9 November 2017
Abstract
Let $M^3$ be an almost coKähler $3$-manifold whose Reeb vector field defines a harmonic map. We prove that if the Cotton tensor of $M^3$ vanishes, then $M^3$ is locally isometric to the product $\mathbb {R}\times N^2(c)$, where $N^2(c)$ denotes a Kähler surface of constant curvature $c$. We construct some examples illustrating our main results.
