$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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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}) $

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