Bi-Lagrangian structures and the space of rays
Differential Geometry
2024-07-10 v2
Abstract
This paper focuses on local curvature invariants associated with bi-Lagrangian structures. We establish several geometric conditions that determine when the canonical connection is flat, building on our previous findings regarding divergence-free webs. Addressing questions raised by Tabachnikov, we provide complete solutions to two problems: the existence of flat bi-Lagrangian structures within the space of rays induced by a pair of hypersurfaces, and the existence of flat bi-Lagrangian structures induced by tangents to Lagrangian curves in the symplectic plane.
Cite
@article{arxiv.2403.10345,
title = {Bi-Lagrangian structures and the space of rays},
author = {Wojciech Domitrz and Marcin Zubilewicz},
journal= {arXiv preprint arXiv:2403.10345},
year = {2024}
}
Comments
31 pages, 2 figures. v2: fixed typos, minor edits (clarifications in Example 1 and Theorem 16)