Left-invariant Riemannian problems on the groups of proper motions of hyperbolic plane and sphere
- Authors: Podobryaev A.V.1, Sachkov Y.L.1
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Affiliations:
- Ailamazyan Program Systems Institute of RAS
- Issue: Vol 95, No 2 (2017)
- Pages: 176-177
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/224973
- DOI: https://doi.org/10.1134/S1064562417020223
- ID: 224973
Cite item
Abstract
On the Lie groups PSL2(ℝ) and SO3 we consider left-invariant Riemannian metrics with two equal eigenvalues. The global optimality of geodesics is investigated. We find the parametrization of geodesics, the cut locus and the equations for the cut time. When the third eigenvalue of a metric tends to the infinity the cut locus and the cut time converge to the cut locus and the cut time of the sub-Riemannian problem.
About the authors
A. V. Podobryaev
Ailamazyan Program Systems Institute of RAS
Author for correspondence.
Email: alex@alex.botik.ru
Russian Federation, 4a Petra-I, s. Veskovo, Pereslavl district, Yaroslavl region, 152021
Yu. L. Sachkov
Ailamazyan Program Systems Institute of RAS
Email: alex@alex.botik.ru
Russian Federation, 4a Petra-I, s. Veskovo, Pereslavl district, Yaroslavl region, 152021