Geodesics and shortest arcs of some sub-Riemannian metrics on the Lie groups $SU(1,1)\times\mathbb{R}$ and $SO_0(2,1)\times\mathbb{R}$ with three-dimensional generating distributions

Irina Zubareva

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arXiv · 2306.03945

Geodesics and shortest arcs of some sub-Riemannian metrics on the Lie groups $SU(1,1)\times\mathbb{R}$ and $SO_0(2,1)\times\mathbb{R}$ with three-dimensional generating distributions

Irina Zubareva

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Abstract

We find geodesics, shortest arcs, cut loci, first conjugate loci for some left-invariant sub-Riemannian metrics on the Lie groups $SU(1,1)\times\mathbb{R}$ and $SO_0(2,1)\times\mathbb{R}$.

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Irina Zubareva. 2023-06-06. Geodesics and shortest arcs of some sub-Riemannian metrics on the Lie groups $SU(1,1)\times\mathbb{R}$ and $SO_0(2,1)\times\mathbb{R}$ with three-dimensional generating distributions. https://arxiv.org/abs/2306.03945

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