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Cotton tensors on almost coKähler 3-manifolds

Volume 120 / 2017

Yaning Wang Annales Polonici Mathematici 120 (2017), 135-148 MSC: Primary 53D15; Secondary 53C25. DOI: 10.4064/ap170410-3-10 Published online: 9 November 2017


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.


  • Yaning WangHenan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control
    School of Mathematics and Information Sciences
    Henan Normal University
    Xinxiang 453007, Henan, P.R. China

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