Geodesic
On the codimension of the abnormal set in step two Carnot groups
ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 18.

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In this article we prove that the codimension of the abnormal set of the endpoint map for certain classes of Carnot groups of step 2 is at least three. Our result applies to all step 2 Carnot groups of dimension up to 7 and is a generalisation of a previous analogous result for step 2 free nilpotent groups.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2018002
Classification : 53C17, 22E25, 14M17
Keywords: Sard property, endpoint map, abnormal curves, Carnot groups, sub-Riemannian geometry

Ottazzi, Alessandro 1 ; Vittone, Davide 1

1 
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Ottazzi, Alessandro; Vittone, Davide. On the codimension of the abnormal set in step two Carnot groups. ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 18. doi : 10.1051/cocv/2018002. http://geodesic.mathdoc.fr/articles/10.1051/cocv/2018002/

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