I. A. Bogaevsky, “Asymptotic behaviour of the sphere and front of a flat sub-Riemannian structure on the Martinet distribution”, Mat. Sb., 2022, Volume 213, Number 5,Pages <nobr>50

This article is cited in 2 papers

Asymptotic behaviour of the sphere and front of a flat sub-Riemannian structure on the Martinet distribution

I. A. Bogaevsky^abc

^a Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
^b Scientific Research Institute for System Analysis of the Russian Academy of Sciences, Moscow, Russia
^c Ailamazyan Program Systems Institute of Russian Academy of Sciences, Ves'kovo, Pereslavl' district, Yaroslavl' oblast', Russia

Abstract: The sphere and front of a flat sub-Riemannian structure on the Martinet distribution are surfaces with nonisolated singularities in three-dimensional space. The sphere is a subset of the front; it is not subanalytic at two antipodal points (the poles). The asymptotic behaviour of the sub-Riemannian sphere and Martinet front are calculated at these points: each surface is approximated by a pair of quasihomogeneous surfaces with distinct sets of weights in a neighbourhood of a pole.
Bibliography: 13 titles.

Keywords: sphere of a sub-Riemannian structure, front of a sub-Riemannian structure, Martinet distribution, exponential map, Jacobi elliptic functions.

MSC: Primary 53C17; Secondary 93B03

Received: 02.02.2021 and 19.01.2022

DOI: 10.4213/sm9560