On three-dimensional conformally flat quasi-Sasakian manifolds
type: Item
instance of: scholarly article
title: On three-dimensional conformally flat quasi-Sasakian manifolds
zbMATH Open document ID: 0881.53011
DOI: 10.1007/BF02093508
published in: Periodica Mathematica Hungarica
publication date: 1998-01-11T00:00:00Z
review text: With the aid of the structure function \(\beta\) of a 3-dimensional quasi-Sasakian manifold \(M\), necessary and sufficient conditions are given for \(M\) to be conformally flat. It is proved that if \(M\) is conformally flat and \(\beta=\text{ const.}\), then (a) \(M\) is locally a product of \(\mathbb{R}\) and a 2-dimensional Kähler-space of constant Gauss curvature, or (b) \(M\) is of constant positive curvature. An example is also given.
Mathematics Subject Classification ID: 53B21
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 1102596
zbMATH Keywords: quasi-Sasakian manifold
zbMATH Keywords: conformally flat manifold
author: Zbigniew Olszak
reviewed by: Lajos Tamássy
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02093508
OpenAlex ID: W2092122369
description: scientific article; zbMATH DE number 1102596