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Differential Geometry

arXiv:dg-ga/9704013 (dg-ga)
[Submitted on 25 Apr 1997]

Title:Chaotic Geodesics in Carnot Groups

Authors:R. Montgomery, M. Shapiro, A. Stolin
View a PDF of the paper titled Chaotic Geodesics in Carnot Groups, by R. Montgomery and 2 other authors
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Abstract: The group of real 4 by 4 upper triangular matrices with 1s on the diagonal has a left-invariant subRiemannian (or Carnot-Caratheodory) structure whose underlying distribution corresponds to the superdiagonal. We prove that the associated subRiemannian geodesic flow is not completely integrable. This provides the first example of a Carnot group (graded nilpotent Lie group with an invariant subRiemannian structure supported on the generating subspace) with a non-integrable geodesic flow. We apply this result to prove that the centralizer for the corresponding quadratic ``quantum'' Hamiltonian in the universal enveloping algebra for this group is ``as small as possible''.
Comments: LaTeX, 10 pages
Subjects: Differential Geometry (math.DG)
MSC classes: 53Cxx, 53C22, 58F07, 58A30
Cite as: arXiv:dg-ga/9704013
  (or arXiv:dg-ga/9704013v1 for this version)
  https://doi.org/10.48550/arXiv.dg-ga/9704013
arXiv-issued DOI via DataCite

Submission history

From: [view email]
[v1] Fri, 25 Apr 1997 00:25:26 UTC (11 KB)
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