Abstract
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.
Citation
Y. Chitour. F. Jean. E. Trélat. "Genericity results for singular curves." J. Differential Geom. 73 (1) 45 - 73, May 2006. https://doi.org/10.4310/jdg/1146680512
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