Toric integrable geodesic flows
Eugene Lerman, Nadya Shirokova
TL;DR
This paper proves that toric integrable geodesic flows on tori necessarily have flat metrics, confirming a conjecture through the study of integrable torus actions on contact manifolds.
Contribution
It establishes that all toric integrable geodesic flows on tori are flat, resolving a conjecture by Toth and Zelditch.
Findings
Toric integrable geodesic flows on tori are flat
Complete classification of such flows under toric symmetry
Confirmation of the Toth and Zelditch conjecture
Abstract
By studying completely integrable torus actions on contact manifolds we prove a conjecture of Toth and Zelditch that toric integrable geodesic flows on tori must have flat metrics.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric and Algebraic Topology · Geometry and complex manifolds · Homotopy and Cohomology in Algebraic Topology