On the approximability and parametrization of preimages of elements of Carnot groups on sub-Lorentzian structures
type: Item
instance of: scholarly article
title: On the approximability and parametrization of preimages of elements of Carnot groups on sub-Lorentzian structures
zbMATH Open document ID: 1494.53037
DOI: 10.1134/S0001434622010175
author: M. Karmanova
published in: Mathematical Notes
publication date: 2022-03-14T00:00:00Z
review text: In this paper the level sets of mappings from one Carnot group to another are studied in the case where the preimages are equipped with a multidimensional sub-Lorentzian structure. Also, a new problem is solved, concerning the accuracy of the order of tangency between a surface and a plane, which is sufficient for both classical and sub-Riemannian approximations. The basic result of the study is the equivalence of such approximations: it is established that, in the case of contact mappings of class \(C^1\), the tangent plane adequately approximates the preimage of an element with respect to the sub-Riemannian metric. A consequence of this result is the derivation of explicit analytical expressions for sub-Riemannian and Riemannian measures of the intersection of a sub-Lorentzian ball and the preimage of an element of a Carnot group.
reviewed by: Liviu Popescu
Mathematics Subject Classification ID: 53C17
zbMATH DE Number: 7488489
zbMATH Keywords: preimage of point
zbMATH Keywords: parametrization of set
zbMATH Keywords: order of tangency
zbMATH Keywords: Carnot group
zbMATH Keywords: sub-Lorentzian structure
zbMATH Keywords: contact mapping
MaRDI profile type: Publication
cites work: MAXIMAL TUBULAR HYPERSURFACES IN MINKOWSKI SPACE
cites work: Reachable sets for the Heisenberg sub-Lorentzian structure on \(\mathbb R^3\). An estimate for the distance function
cites work: Geodesics on \({\mathbb{H}}\)-type quaternion groups with sub-Lorentzian metric and their physical interpretation
cites work: Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
cites work: Carnot-Carathéodory metrics and quasiisometries of symmetric spaces of rank 1
cites work: Q3517273
cites work: On local metric characteristics of level sets of \(C_H^1\)-mappings of Carnot manifolds
cites work: The polynomial sub-Riemannian differentiability of some Hölder mappings of Carnot groups
full work available at URL: s0001434622010175
OpenAlex ID: W4213444081
description: scientific article; zbMATH DE number 7488489