Locally symmetric almost coK\"{a}hler 5-manifolds with K\"{a}hlerian leaves
Bull. Korean Math. Soc. 2018 Vol. 55, No. 3, 789-798
Published online May 31, 2018
Yaning Wang
Henan Normal University
Abstract : Let $M$ be a compact almost coK\"{a}hler $5$-manifold with K\"{a}hler\-ian leaves. In this paper, we prove that $M$ is locally symmetric if and only if it is locally isometric to a Riemannian product of a unit circle $S^1$ and a locally symmetric compact K\"{a}hler $4$-manifold.
Keywords : almost coK\"{a}hler $5$-manifold, local symmetry
MSC numbers : Primary 53D15; Secondary 53C25
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