Lie contact structures and normal Cartan connections
type: Item
instance of: scholarly article
title: Lie contact structures and normal Cartan connections
zbMATH Open document ID: 0732.53023
published in: Kodai Mathematical Journal
publication date: 1991-01-01T00:00:00Z
review text: Let N be a (2n-1)-dimensional differentiable manifold. A Lie contact structure on N is defined to be a certain special reduction of the linear frame bundle over N [\textit{H. Sato} and \textit{K. Yamaguchi}, Geometry of manifolds, Coll. Pap. 35th Symp. Differ. Geom., Matsumoto/Japan 1988, Perspect. Math. 8, 191-238 (1989; Zbl 0705.53019)]. One of the important examples of such structures is that given on the unit tangent bundle \(T_ 1M\) of a Riemannian manifold M. Following the connection theory by \textit{N. Tanaka} [Hokkaido Math. J. 8, 23-84 (1979; Zbl 0409.17013)], the author constructs a normal Cartan connection (so-called Tanaka connection) corresponding to a Lie contact structure. Next, he proves that the normal connection determines the structure completely.
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 53C05
zbMATH DE Number: 4210971
zbMATH Keywords: Lie contact structure
zbMATH Keywords: Cartan connection
zbMATH Keywords: Tanaka connection
author: Reiko Miyaoka
reviewed by: Zbigniew Olszak
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138039338
OpenAlex ID: W2066128996
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DOI: 10.2996/KMJ/1138039338
description: scientific article; zbMATH DE number 4210971