Genericity results for singular curves
Chitour, Y. ; Jean, F. ; Trélat, E.
J. Differential Geom., Tome 72 (2006) no. 1, p. 45-73 / Harvested from Project Euclid
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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.
Publié le : 2006-05-14
Classification:  
@article{1146680512,
     author = {Chitour, Y. and Jean, F. and Tr\'elat, E.},
     title = {Genericity results for singular curves},
     journal = {J. Differential Geom.},
     volume = {72},
     number = {1},
     year = {2006},
     pages = { 45-73},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1146680512}
}

Chitour, Y.; Jean, F.; Trélat, E. Genericity results for singular curves. J. Differential Geom., Tome 72 (2006) no. 1, pp.  45-73. http://gdmltest.u-ga.fr/item/1146680512/