Volume 28, 2022
|Number of page(s)||30|
|Published online||22 December 2022|
Sub-Riemannian geodesics on SL(2,ℝ)
Department of Mathematics, Iowa State University,
2 Department of Mathematics, University of California Santa Barbara, Santa Barbara, CA 93106-3080, USA
* Corresponding author: email@example.com
Accepted: 13 October 2022
We explicitly describe the length minimizing geodesics for a sub-Riemannian structure of the elliptic type defined on SL(2, ℝ). Our method uses a symmetry reduction which translates the problem into a Riemannian problem on a two dimensional quotient space, on which projections of geodesics can be easily visualized. As a byproduct, we obtain an alternative derivation of the characterization of the cut-locus. We use classification results for three dimensional right invariant sub-Riemannian structures on Lie groups to identify exactly automorphic structures on which our results apply.
Mathematics Subject Classification: 54C17 / 53C22 / 57S20 / 22E15
Key words: Sub-Riemannian Geometry / Lie group SL(2,ℝ) / symmetry reduction / optimal synthesis
© The authors. Published by EDP Sciences, SMAI 2022
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