GENERIC SINGULARITIES OF SUB-RIEMANNIAN METRICS ON R(3)

Authors
AGRACHEV A ELALAOUI EC GAUTHIER JP KUPKA I
Citation
A. Agrachev et al., GENERIC SINGULARITIES OF SUB-RIEMANNIAN METRICS ON R(3), Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 322(4), 1996, pp. 377-384
Citations number
7
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Comptes rendus de l'Academie des sciences. Serie 1, Mathematique → ACNP
ISSN journal
07644442
Volume
322
Issue
4
Year of publication
1996
Pages
377 - 384
Database
ISI
SICI code
0764-4442(1996)322:4<377:GSOSMO>2.0.ZU;2-Q
Abstract
The purpose of this Note is the local study of Sub-Riemannian metrics in the most simple case: dimension 3 and contact distribution. Even in this simple case, there exist fundamental differences with Riemannian metrics. For instance, conjugate points appear, arbitrarily close to the origin. We give the full local, generic, classification of singula rities that can happen for conjugate loci, cut loci and spheres.