TY - JOUR

T1 - Privileged Coordinates for Carnot–Carathéodory Spaces of Lower Smoothness

AU - Basalaev, S. G.

PY - 2020/9/1

Y1 - 2020/9/1

N2 - We describe classes of local coordinates onthe Carnot–Carathéodory spaces of lower smoothnesswhich permit the homogeneous approximation of quasimetrics and basis vector fields.We establish the minimal smoothnessthat is required for these classes to coincide withthe class of the already-described privileged coordinatesin the infinite smoothness case.Moreover,we apply these results to provethe analogs of the available theoremsin the case of the canonical coordinates of the second kind.Also, we prove some convergence theorems in quasimetric spaces.

AB - We describe classes of local coordinates onthe Carnot–Carathéodory spaces of lower smoothnesswhich permit the homogeneous approximation of quasimetrics and basis vector fields.We establish the minimal smoothnessthat is required for these classes to coincide withthe class of the already-described privileged coordinatesin the infinite smoothness case.Moreover,we apply these results to provethe analogs of the available theoremsin the case of the canonical coordinates of the second kind.Also, we prove some convergence theorems in quasimetric spaces.

KW - 514.77:517.28

KW - nilpotent tangent cone

KW - privileged coordinates

KW - sub-Riemannian geometry

KW - APPROXIMATION THEOREM

KW - DIFFERENTIABILITY

KW - VECTOR-FIELDS

KW - GEOMETRY

UR - http://www.scopus.com/inward/record.url?scp=85091676741&partnerID=8YFLogxK

U2 - 10.1134/S0037446620050018

DO - 10.1134/S0037446620050018

M3 - Article

AN - SCOPUS:85091676741

VL - 61

SP - 763

EP - 777

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 5

ER -