Sub-riemannian geometry from intrinsic viewpoint

Abstract : Gromov proposed to extract the (di erential) geometric content of a sub-riemannian space exclusively from its Carnot-Carath eodory 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 di erential 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

Cited literature [31 references]  Display  Hide  Download

https://hal-confremo.archives-ouvertes.fr/hal-00700925
Contributor : Ali Fardoun <>
Submitted on : Tuesday, June 19, 2012 - 11:01:50 AM
Last modification on : Tuesday, June 19, 2012 - 5:16:02 PM
Long-term archiving on : Thursday, December 15, 2016 - 3:50:06 PM

File

CIMPABeyrouth12.Buliga2.pdf
Explicit agreement for this submission

Identifiers

  • HAL Id : hal-00700925, version 2

Collections

Citation

Marius Buliga. Sub-riemannian geometry from intrinsic viewpoint. École de recherche CIMPA : Géométrie sous-riemannienne, Jan 2012, BEYROUTH, Lebanon. ⟨hal-00700925v2⟩

Share

Metrics

Record views

289

Files downloads

171