Some remarks on \(R\)-contact flows
type: Item
instance of: scholarly article
title: Some remarks on \(R\)-contact flows
zbMATH Open document ID: 0820.53042
DOI: 10.1007/BF00773454
author: Philippe Rukimbira
published in: Annals of Global Analysis and Geometry
publication date: 1995-03-01T00:00:00Z
review text: A flow \({\mathfrak F} = (M,{\mathfrak F})\) (tangentially oriented 1-dimensional foliation) is said to be Riemannian if there exists a Riemannian metric \(g\) on \(M\) such that for any vector field \(X\) tangent to \(\mathfrak F\) and \(U\), \(V\) orthogonal to \(\mathfrak F\), one has \((L\times g)(U,V) = 0\). Then the metric \(g\) is called a bundle-like metric. A contact manifold \((M,\alpha)\) is said to be an \(R\)-contact manifold if its characteristic vector field \(\xi\) of \(\alpha\) defines a Riemannian flow. The author obtains several results concerning the structures of the set \(F_ \xi\) of periodic points of \(\xi\) and the curvature of the \(R\)-metrics. Furthermore, the author proves that no torus \(T^{2n + 1}\) can carry an \(R\)-contact metric, which generalizes a result of \textit{D. E. Blair} [Contact manifolds in Riemannian geometry, Lect. Notes Math. 509, Springer Verlag (1976; Zbl 0319.53026)].
reviewed by: Kouei Sekigawa
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 37C85
zbMATH DE Number: 727087
zbMATH Keywords: \(R\)-contact harmonic forms
zbMATH Keywords: nonpositive sectional curvature
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 727087