Metabelian distributions and sub-Riemannian geodesics
Abstract
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 , α {C^{1,\alpha}} , for some α ∈ ( 0 , 1 ) {\alpha\in(0,1)} .
Fields of Study & Subjects
Morphological variations and asymmetry
advanced mathematical theories
Statistical Mechanics and Entropy
Publication details
- Journal / source
- Advances in Calculus of Variations
- Publisher
- Walter de Gruyter GmbH
- Volume
- 19
- Issue
- 3
- Pages
- 423–433
- Publication date
- 20 April 2026
- Language
- EN