Open Access
May 2006 Genericity results for singular curves
Y. Chitour, F. Jean, E. Trélat
J. Differential Geom. 73(1): 45-73 (May 2006). DOI: 10.4310/jdg/1146680512


Let M be a smooth manifold and Dm, m ≥ 2, be the set of rank m distributions on M endowed with the Whitney C topology. We show the existence of an open set Om dense in Dm, so that every nontrivial singular curve of a distribution D of Om is of minimal order and of corank one. In particular, for m > 3, every distribution of Om does not admit nontrivial rigid curves. As a consequence, for generic sub-Riemannian structures of rank greater than or equal to three, there do not exist nontrivial minimizing singular curves.


Download Citation

Y. Chitour. F. Jean. E. Trélat. "Genericity results for singular curves." J. Differential Geom. 73 (1) 45 - 73, May 2006.


Published: May 2006
First available in Project Euclid: 3 May 2006

zbMATH: 1102.53019
MathSciNet: MR2217519
Digital Object Identifier: 10.4310/jdg/1146680512

Rights: Copyright © 2006 Lehigh University

Vol.73 • No. 1 • May 2006
Back to Top