Sub-riemannian geometry from intrinsic viewpoint

Abstract : Gromov proposed to extract the (differential) geometric content of a sub-riemannian space exclusively from its Carnot-Caratheodory distance. One of the most striking features of a regular sub-riemannian space is that it has at any point a metric tangent space with the algebraic structure of a Carnot group, hence a homogeneous Lie group. Siebert characterizes homogeneous Lie groups as locally compact groups admitting a contracting and continuous one-parameter group of automorphisms. Siebert result has not a metric character. In these notes I show that sub-riemannian geometry may be described by about 12 axioms, without using any a priori given differential structure, but using dilation structures instead. Dilation structures bring forth the other intrinsic ingredient, namely the dilations, thus blending Gromov metric point of view with Siebert algebraic one.
Document type :
Conference papers
Complete list of metadatas

https://hal-confremo.archives-ouvertes.fr/hal-00700925
Contributor : Ali Fardoun <>
Submitted on : Thursday, May 24, 2012 - 11:49:29 AM
Last modification on : Friday, February 6, 2015 - 12:54:20 PM
Long-term archiving on : Friday, November 30, 2012 - 12:10:15 PM

File

CIMPABeyrouth12.Buliga.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00700925, version 1

Citation

Marius Buliga. Sub-riemannian geometry from intrinsic viewpoint. École de recherche CIMPA : Géométrie sous-riemannienne, Jan 2012, BEYROUTH, Lebanon. ⟨hal-00700925v1⟩

Share

Metrics

Record views

46

Files downloads

21