Conformally flat almost Kenmotsu 3-manifolds
type: Item
instance of: scholarly article
title: Conformally flat almost Kenmotsu 3-manifolds
zbMATH Open document ID: 1378.53094
author: Yaning Wang
published in: Mediterranean Journal of Mathematics
publication date: 2017-11-09T00:00:00Z
review text: A Riemannian manifold is called conformally flat if its metric is conformally related to a flat Euclidean metric. In the present paper the author gives a necessary and sufficient condition for an almost Kenmotsu 3-manifold to be conformally flat, by virtue of a system of partial differential equations,. He also proves that an almost Kenmotsu 3-H-manifold with scalar curvature invariant along the Reeb vector field is conformally flat if and only if it is locally isometric to either the hyperbolic space \(\mathbb{H}^3 (-1)\) or the Riemannian product \(\mathbb{H}^2 (-4)\times\mathbb R\). Some concrete examples verifying main results are also given.
reviewed by: Andreas Arvanitoyeorgos
Mathematics Subject Classification ID: 53D15
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 6804282
zbMATH Keywords: almost Kenmotsu 3-manifold
zbMATH Keywords: conformally flat
zbMATH Keywords: harmonic Reeb vector field
MaRDI profile type: Publication
full work available at URL: s00009-017-0984-9
OpenAlex ID: W2747963793
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DOI: 10.1007/S00009-017-0984-9
description: scientific article; zbMATH DE number 6804282