Geodesics of nonholonomic left-invariant intrinsic metrics on the Heisenberg group and isoperimetric curves on the Minkowski plane
type: Item
instance of: scholarly article
title: Geodesics of nonholonomic left-invariant intrinsic metrics on the Heisenberg group and isoperimetric curves on the Minkowski plane
zbMATH Open document ID: 0834.53049
DOI: 10.1007/BF02104943
published in: Siberian Mathematical Journal
publication date: 1995-09-18T00:00:00Z
review text: Let \(H\) be the Heisenberg group of real upper-triangular \((3 \times 3)\)- matrices with unity entries in the principal diagonal and let \(d_c\) be an arbitrary nonholonomic metric on \(H\). Among other things the author proves that a curve in \((H,d_c)\) starting at the unity \(e \in H\) is a geodesic if and only if it satisfies Pontryagin's maximum principle for an associated time-optimal control problem.
Mathematics Subject Classification ID: 53C70
Mathematics Subject Classification ID: 22E30
Mathematics Subject Classification ID: 49J20
zbMATH DE Number: 794611
zbMATH Keywords: Minkowski plane
zbMATH Keywords: geodesics
zbMATH Keywords: optimal controls
zbMATH Keywords: Heisenberg group
author: V. N. Berestovskij
reviewed by: Dumitru Motreanu
MaRDI profile type: Publication
cites work: Q3825006
cites work: Q5719719
cites work: Q4711784
cites work: Reduction of nonholonomic variation problems to isoperimetric ones and connections in principal bundles
cites work: On a constrained variational problem and the space of horizontal paths
full work available at URL: https://doi.org/10.1007/bf02104943
OpenAlex ID: W2046838141
description: scientific article; zbMATH DE number 794611