Geodesics and Shortest Arcs of Some Sub-Riemannian Metrics on the Lie Groups $ \operatorname{SU}(1,1)\times 𝕉 $ and $ \operatorname{SO}_{0}(2,1)\times 𝕉 $ with Three-Dimensional Generating Distributions

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发表日期：

2024年3月25日

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I. A. Zubareva

摘要

We find geodesics, shortest arcs, cut loci, and first conjugate loci for some left-invariant sub-Riemannian metrics on the Lie groups $ \operatorname{SU}(1,1)\times 𝕉 $ and $ \operatorname{SO}_{0}(2,1)\times 𝕉 $ .

Geodesics and Shortest Arcs of Some Sub-Riemannian Metrics on the Lie Groups \( \operatorname{SU}(1,1)\times 𝕉 \) and \( \operatorname{SO}_{0}(2,1)\times 𝕉 \) with Three-Dimensional Generating Distributions

摘要