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Collapsed limits of
compact Heisenberg manifolds with sub-Riemannian metrics
Kenshiro Tashiro |
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Vol. 329 (2024), No. 1, 165–181
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Abstract |
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We show that every collapsed Gromov–Hausdorff limit of compact Heisenberg manifolds endowed with left-invariant Riemannian/sub-Riemannian metrics is isometric to a flat torus. We say that a sequence of sub-Riemannian manifolds collapses if their total measure with respect to Popp’s volume converges to zero. |
Keywords
Heisenberg group, sub-Riemannian geometry
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Mathematical Subject Classification
Primary: 53C17
Secondary: 20F18, 28A78
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Milestones
Received: 28 July 2021
Revised: 12 July 2023
Accepted: 11 May 2024
Published: 12 June 2024
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Authors |
| Kenshiro Tashiro | |
| Mathematical Institute Tohoku University Sendai Japan |
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| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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