Sub-Riemannian structures on 3D lie groups View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2012-01

AUTHORS

A. Agrachev, D. Barilari

ABSTRACT

We give a complete classification of left-invariant sub-Riemannian structures on three-dimensional Lie groups in terms of the basic differential invariants. As a consequence, we explicitly find a sub-Riemannian isometry between the nonisomorphic Lie groups SL(2) and A+() × S1, where A+() denotes the group of orientation preserving affine maps on the real line. More... »

PAGES

21-44

References to SciGraph publications

  • 1994-02. The tangent space in sub-riemannian geometry in JOURNAL OF MATHEMATICAL SCIENCES
  • 2000-07. On Sub-Riemannian Caustics and Wave Fronts for Contact Distributions in the Three-Space in JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS
  • 1940-12. Über Systeme von liearren partiellen Differentialgleichungen erster Ordnung in MATHEMATISCHE ANNALEN
  • 1996-10. Sub-Riemannian homogeneous spaces in dimensions 3 and 4 in GEOMETRIAE DEDICATA
  • 1996-07. Exponential mappings for contact sub-Riemannian structures in JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS
  • 1933-12. Sur la géométrie pseudo-conforme des hypersurfaces de l'espace de deux variables complexes in ANNALI DI MATEMATICA PURA ED APPLICATA (1923 -)
  • Identifiers

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    http://scigraph.springernature.com/pub.10.1007/s10883-012-9133-8

    DOI

    http://dx.doi.org/10.1007/s10883-012-9133-8

    DIMENSIONS

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