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arXiv · 2405.14997

Metabelian distributions and sub-Riemannian geodesics

Enrico Le Donne·Nicola Paddeu·Alessandro Socionovo
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Abstract

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 $r$, the projection of strictly singular trajectories to some $r$-dimensional manifold must remain within an analytic variety. As a consequence, for rank-2 metabelian distributions, geodesics are of class $C^1$.

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Enrico Le Donne, Nicola Paddeu, Alessandro Socionovo. 2024-05-23. Metabelian distributions and sub-Riemannian geodesics. https://arxiv.org/abs/2405.14997

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