Left-invariant Sub-Riemannian Engel structures: abnormal geodesics and\n integrability

2016/11/11 by Ivan Beschastnyi, Beschastnyi, Ivan, Alexandr Medvedev +1 · 1 citation
Mathematics · Physics and Astronomy · #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Waves and Solitons #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.1611.03634

openalex publication_date 2016/11/11 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We provide the first known family of examples of integrable homogeneous\nsub-Riemannian structures admitting strictly abnormal geodesics. These examples\nwere obtained through the analysis of the equivalence problem for\nsub-Riemannian Engel structures. We formulate a criterion of strict abnormality\nin terms of structure functions of a canonical frame on a sub-Riemannian Engel\nmanifold as well as estimates on conjugate times.\n

Cited by

• Engel CR submanifolds of ℂ³

Related

• Riemannian properties of Engel structures
• Geometry and dynamics of Engel structures
• Strictly abnormal geodesics with a degeneracy point in the interior of their domain
• Lagrangian Engel Structures
• Integrable sub-Riemannian geodesic flows on the special orthogonal group