Lie contact structures and conformal structures
type: Item
instance of: scholarly article
title: Lie contact structures and conformal structures
zbMATH Open document ID: 0732.53024
published in: Kodai Mathematical Journal
publication date: 1991-01-01T00:00:00Z
review text: The author continues investigations of Lie contact structures [ibid., 13- 41 (1991; see the review above)] and computes the curvature K of the Tanaka connection associated to the Lie contact structure on a unit tangent bundle \(T_ 1M\) of a Riemannian manifold M. This curvature is strictly related to Weyl's conformal curvature of M. When \(K=0\), \(T_ M\) is said to be flat; in this case the structure is locally equivalent to that on the model space \(T_ 1{\mathbb{S}}^ n\). It is proved that if \(\tilde f:\) \(T_ 1M\to T_ 1M'\) is a bundle map preserving the Lie curvature K, then the induced map f: \(M\to M'\) preserves the conformal curvature. Especially, the Lie flatness of the Tanaka connection of \(T_ 1M\) can be characterized by the conformal flatness of M.
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 53C05
zbMATH DE Number: 4210972
zbMATH Keywords: Lie contact structures
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/1138039339
OpenAlex ID: W2067895729
cites work: Tautness and Lie sphere geometry
cites work: Lie contact structures and normal Cartan connections
cites work: Q4281138
cites work: Theory of conformal connections
cites work: Lusin functions on product spaces
cites work: Q3485556
cites work: On the differential geometry of tangent bundles of Riemannian manifolds
cites work: On the equivalence problems associated with simple graded Lie algebras
DOI: 10.2996/KMJ/1138039339
description: scientific article; zbMATH DE number 4210972