1 citations · 2 across the 6 of their papers we have counts for
7 papers
Sard property for rank 2 polarizations in metabelian Lie groups
Enrico Le Donne, Antonio Lerario, Luca Nalon +2
We provide sharp bounds on the dimension of the abnormal set for rank polarizations on metabelian Lie groups, establishing the Sard property for the end-point map of such group…
Normal Curves in Sub-Finsler Lie Groups: Branching for Strongly Convex Norms and Face Stability for Polyhedral Norms
Enrico Le Donne, Sebastiano Nicolussi Golo, Nicola Paddeu
We consider Lie groups equipped with left-invariant subbundles of their tangent bundles and norms on them. On these sub-Finsler structures, we study the normal curves in the sense…
Strictly abnormal geodesics with a degeneracy point in the interior of their domain
Nicola Paddeu, Alessandro Socionovo
In this article, we study abnormal curves in a family of sub-Riemannian manifolds of rank 2. We focus on abnormal curves whose lifts to the cotangent bundle annihilate, at an inter…
Hypergenerated Carnot groups
Enrico Le Donne, Luca Nalon, Nicola Paddeu +1
In this paper we provide an algebraic characterization of those stratified groups in which boundaries with locally constant normal are locally flat. We show that these groups, whic…
Metabelian distributions and sub-Riemannian geodesics
Enrico Le Donne, Nicola Paddeu, Alessandro Socionovo
We begin by characterizing metabelian distributions in terms of principal bundle structures. Then, we prove that in sub-Riemannian manifolds with metabelian distributions of rank $…
Escape from compact sets of normal curves in Carnot groups
Enrico Le Donne, Nicola Paddeu
In the setting of subFinsler Carnot groups, we consider curves that satisfy the normal equation coming from the Pontryagin Maximum Principle. We show that, unless it is constant, e…
Sympletic reduction of the sub-Riemannian geodesic flow for metabelian nilpotent groups
Alejandro Bravo-Doddoli, Enrico Le Donne, Nicola Paddeu
We consider nilpotent Lie groups for which the derived subgroup is abelian. We equip them with subRiemannian metrics and we study the normal Hamiltonian flow on the cotangent bundl…