ABNORMAL SUBANALYTIC DISTRIBUTIONS IN SUB-RIEMANNIAN GEOMETRY
Résumé
We present a description of singular horizontal curves of a bracket generating analytic distribution in terms of the projections of the orbits of some isotropic subanalytic singular distribution defined on the nonzero annihilator of the initial distribution in the cotangent bundle. We expect this presentation to be useful in the context of the Sard Conjecture in sub-Riemannian geometry. We provide an evidence by showing that the Sard Conjecture holds true for trajectories that remains in a single stratum, and by showing the minimal rank Sard Conjecture for Carnot groups. In a follow-up paper, we use our description to obtain, under an additional assumption on the constructed subanalytic singular distribution, a proof of the minimal rank Sard conjecture in the analytic category.
Domaines
Géométrie différentielle [math.DG]
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AbnormalSubanDistr_and_MinimalSard-PartI-Version2.pdf (606.23 Ko)
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