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Length spectra of
sub-Riemannian metrics on compact Lie groups
András Domokos, Matthew Krauel, Vincent Pigno, Corey Shanbrom and Michael VanValkenburgh |
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Vol. 296 (2018), No. 2, 321–340
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Abstract |
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Length spectra for Riemannian metrics have been well studied, while sub-Riemannian length spectra remain largely unexplored. Here we give the length spectrum for a canonical sub-Riemannian structure attached to any compact Lie group by restricting its Killing form to the sum of the root spaces. Surprisingly, the shortest loops are the same in both the Riemannian and sub-Riemannian cases. We provide specific calculations for and . |
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Keywords
sub-Riemannian geometry, geodesics, root systems, compact
Lie groups
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Mathematical Subject Classification 2010
Primary: 53C17, 53C22
Secondary: 22E30, 51N30
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Milestones
Received: 7 April 2017
Revised: 11 December 2017
Accepted: 2 March 2018
Published: 16 July 2018
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Authors |
| András Domokos | |
| Department of Mathematics and
Statistics California State University Sacramento 6000 J Street Sacramento, CA 95819 United States |
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| Matthew Krauel | |
| Department of Mathematics and
Statistics California State University Sacramento 6000 J Street Sacramento, CA 95819 United States |
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| Vincent Pigno | |
| Department of Mathematics and
Statistics California State University Sacramento 6000 J Street Sacramento, CA 95819 United States |
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| Corey Shanbrom | |
| Department of Mathematics and
Statistics California State University Sacramento 6000 J Street Sacramento, CA 95819 United States |
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| Michael VanValkenburgh | |
| Department of Mathematics and
Statistics California State University, Sacramento 6000 J Street Sacramento, CA 95819 United States |
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