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JOURNALS // Sibirskii Matematicheskii Zhurnal // Archive

Sibirsk. Mat. Zh., 2014 Volume 55, Number 5, Pages 1160–1166 (Mi smj2594)

This article is cited in 1 paper

The normal sub-Riemannian geodesic flow on $E(2)$ generated by a left-invariant metric and a right-invariant distribution

A. D. Mazhitova

Al-Farabi Kazakh National University, Almaty, Kazakhstan

Abstract: We consider a sub-Riemannian problem on the three-dimensional solvable Lie group $E(2)$ endowed with a left-invariant metric and a right-invariant distribution. The problem is based on construction of a Hamilton structure for the given metric by the Pontryagin maximum principle.

Keywords: sub-Riemannian geometry, right-invariant metric, Hamiltonian, geodesic.

UDC: 514.7

Received: 25.11.2013


 English version:
Siberian Mathematical Journal, 2014, 55:5, 948–953

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© Steklov Math. Inst. of RAS, 2025