On the behavior of geodesics of left-invariant sub-Riemannian metrics on the group $ \operatorname{Aff}_{0}(\mathbb{R}) \times \operatorname{Aff}_{0}(\mathbb{R}) $

On the behavior of geodesics of left-invariant sub-Riemannian metrics on the group $ \operatorname{Aff}_{0}(\mathbb{R}) \times \operatorname{Aff}_{0}(\mathbb{R}) $

In this paper, we study geodesics of left-invariant sub-Riemannian metrics on the Cartesian square of a connected two-dimensional non-commutative Lie group, where the metric is determined by the inner product on a two-dimensional generating subspace of the corresponding Lie algebra. It is proven tha...

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Bibliographic Details
Main Authors: Yuriĭ G. Nikonorov, Irina A. Zubareva
Format: Article
Language:English
Published: AIMS Press 2025-01-01
Series:Electronic Research Archive
Subjects:
extremal
generating subspace of a lie algebra
hamiltonian system
kovalevskaya exponents
left-invariant sub-riemannian metric
non-commutative two-dimensional lie group
sub-riemannian geodesic
Online Access:https://www.aimspress.com/article/doi/10.3934/era.2025010
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