From the 1 of 5 linked papers with an AI index.
5 papers
Sard property for rank 2 polarizations in metabelian Lie groups
Enrico Le Donne, Antonio Lerario, Luca Nalon +2
The paper establishes dimension bounds for abnormal and Goh‑abnormal sets in rank‑2 polarized metabelian Lie groups, proving that the endpoint map satisfies the Sard property and t…
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 $…