2013/01/13 by Boris Doubrov, Doubrov, Boris, Igor Zelenko +1
Mathematics · Physics and Astronomy · #34A26 #34C14 #53A55 #53C17 #58A30 #Advanced Algebra and Geometry #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1301.2797
openalex publication_date 2013/01/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We demonstrate how the novel approach to the local geometry of structures of nonholonomic nature, originated by Andrei Agrachev, works in the following two situations: rank 2 distributions of maximal class in Rn with non-zero generalized Wilczynski invariants and rank 2 distributions of maximal class in Rn with additional structures such as affine control system with one input spanning these distributions, sub-(pseudo)Riemannian structures etc. The common feature of these two situations is that each abnormal extremal (of the underlying rank 2 distribution) possesses a distinguished parametrization. This fact allows one to construct the canonical frame on a (2n-3)-dimensional bundle in both situations for arbitrary n greater than 4. The moduli spaces of the most symmetric models for both situations are described as well. The relation of our results to the divergence equivalence of Lagrangians of higher order is given