June 12, 2024Open Access

Collapsed limits of compact Heisenberg manifolds with sub-Riemannian metrics

Key Points

Key points are not available for this paper at this time.

Abstract

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.

Connected Papers

Building similarity graph...

Analyzing shared references across papers

Discussion

Cite this study

Kenshiro Tashiro (Wed,) studied this question.

synapsesocial.com/papers/68e651bbb6db6435875e1cf4 — DOI: https://doi.org/10.2140/pjm.2024.329.165

Also consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

Teichmüller theory and collapse of flat manifolds· 2018 · 12 citations
Hausdorff Convergence of Riemannian Manifolds and Its Applications· 2018 · 19 citations
The spectrum of the Laplacian on Riemannian Heisenberg manifolds.· 1986 · 129 citations
A Tour of Subriemannian Geometries, Their Geodesics and Applications· 2006 · 967 citations
Teichmüller theory and collapse of flat manifolds· 2018 · 12 citations

Authors

Kenshiro Tashiro

Okinawa Institute of Science and Technology Graduate University

Journals

Pacific Journal of Mathematics

Actions

Institutions

Tohoku University

References and Citations

Connected Papers

Building similarity graph...

Analyzing shared references across papers

Collapsed limits of compact Heisenberg manifolds with sub-Riemannian metrics

Key Points

Abstract

Citation Network

Connected Papers

Discussion

Cite this study

Also consider

Authors

Journals

Actions

Institutions

References and Citations

Citation Network

Connected Papers

Discussion

Also consider