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arXiv · 2403.10345

Bi-Lagrangian structures and the space of rays

Wojciech Domitrz·Marcin Zubilewicz
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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.

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Wojciech Domitrz, Marcin Zubilewicz. 2024-03-15. Bi-Lagrangian structures and the space of rays. https://arxiv.org/abs/2403.10345

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