Isometries of Carnot Groups and Sub-Finsler Homogeneous Manifolds View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2016-01

AUTHORS

Enrico Le Donne, Alessandro Ottazzi

ABSTRACT

We show that isometries between open sets of Carnot groups are affine. This result generalizes a result of Hamenstädt. Our proof does not rely on her proof. We show that each isometry of a sub-Riemannian manifold is determined by the horizontal differential at one point. We then extend the result to sub-Finsler homogeneous manifolds. We discuss the regularity of isometries of homogeneous manifolds equipped with homogeneous distances that induce the manifold topology. More... »

PAGES

330-345

References to SciGraph publications

  • 1989-03. Homogeneous manifolds with intrinsic metric. II in SIBERIAN MATHEMATICAL JOURNAL
  • 2013. Sub-Finsler Geometry and Finite Propagation Speed in TRENDS IN HARMONIC ANALYSIS
  • 1995-03. The differential of a quasi-conformal mapping of a Carnot-Caratheodory space in GEOMETRIC AND FUNCTIONAL ANALYSIS
  • 1988-11. Homogeneous manifolds with intrinsic metric. I in SIBERIAN MATHEMATICAL JOURNAL
  • 2017-07. Sub-Finsler Structures from the Time-Optimal Control Viewpoint for some Nilpotent Distributions in JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS
  • 2012-01. Sub-Riemannian structures on 3D lie groups in JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS
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    http://scigraph.springernature.com/pub.10.1007/s12220-014-9552-8

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    http://dx.doi.org/10.1007/s12220-014-9552-8

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