Rigidity of integral curves of rank 2 distributions
type: Item
instance of: scholarly article
title: Rigidity of integral curves of rank 2 distributions
zbMATH Open document ID: 0807.58007
DOI: 10.1007/BF01232676
author: Robert L. Bryant
author: Lucas Hsu
published in: Inventiones Mathematicae
publication date: 1995-02-28T00:00:00Z
full work available at URL: https://eudml.org/doc/144154
review text: Let \(\Omega_ D(p,q)\) be the space consisting of differentiable curves in a manifold \(M\) joining \(p\) to \(q\) and staying tangent to a distribution \(D\). At most of its points, \(\Omega_ D(p,q)\) after being endowed with an appropriate topology, behaves very much like an infinite dimensional manifold. However, there are sometimes special curves \(\gamma \in \Omega_ D(p,q)\) around which the local structure of \(\Omega_ D(p,q)\) is drastically different. The authors show that for ``most'' distributions \(D\) of rank 2, such special curves always occur. In particular, the authors are interested in so-called non-regular curves \(\gamma\) at which \(\Omega_ D(p,q)\) fails to be a smooth manifold when endowed with the natural \(C'\)-topology, and where the natural candidate for the tangent space \(T_ \gamma \Omega_ D(p,q)\) fails to be the true tangent space. The paper concentrates on the case of rigid \(D\)-curves, that is, points \(\gamma \in \Omega_ D(p,q)\) which are essentially isolated.
Mathematics Subject Classification ID: 58D99
Mathematics Subject Classification ID: 58D10
Mathematics Subject Classification ID: 58B99
zbMATH DE Number: 549655
zbMATH Keywords: space of differentiable curves
zbMATH Keywords: rigid curves
zbMATH Keywords: distribution
zbMATH Keywords: infinite dimensional manifold
zbMATH Keywords: non-regular curves
reviewed by: Anthony D. Osborne
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 549655