Privileged coordinates for carnot–carathéodory spaces of lower smoothness

S. G. Basalaev<sup>ab

a</sup> Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Novosibirsk State University

Abstract: We describe classes of local coordinates on the Carnot–Carathéodory spaces of lower smoothness which permit the homogeneous approximation of quasimetrics and basis vector fields. We establish the minimal smoothness that is required for these classes to coincide with the class of the already-described privileged coordinates in the infinite smoothness case. Moreover, we apply these results to prove the analogs of the available theorems in the case of the canonical coordinates of the second kind. Also, we prove some convergence theorems in quasimetric spaces.

Keywords: sub-Riemannian geometry, nilpotent tangent cone, privileged coordinates.

UDC: 514.77+517.28

MSC: 35R30

Received: 30.07.2018
Revised: 11.09.2018
Accepted: 17.10.2018

DOI: 10.33048/smzh.2020.61.501

 English version: Siberian Mathematical Journal, 2020, 61:5, 763–777

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