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Bi-Lagrangian structures and the space of rays

2024/03/15 by Domitrz, Wojciech, Zubilewicz, Marcin
#53A60 #53D12 #78A05 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.10345

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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