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arXiv · 2408.13873

Metric Lines in the Special Euclidean group on the plane

Y. Wang·S. Ku·A. Bravo-Doddoli
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Abstract

The Special Euclidean group on the plane $SE(2)$ has the left-invariant sub-Riemannian structure. Every sub-Riemannian manifold possesses a Hamiltonian function governing the sub-Riemannian geodesic flow. Two natural questions are: What are the necessary conditions for periodic sub-Riemannian geodesics? What geodesics are the metric lines in SE(2)? We answer both questions, and our method for the second is an alternative proof using the Hamilton-Jacobi theory.

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Y. Wang, S. Ku, A. Bravo-Doddoli. 2024-08-25. Metric Lines in the Special Euclidean group on the plane. https://doi.org/10.2140/involve.2026.19.471

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