Canonical curves and Kropina metrics in Lagrangian contact geometry

Canonical curves and Kropina metrics in Lagrangian contact geometry

Nonlinearity 37 (2024), 015007 We present a Fefferman-type construction from Lagrangian contact to conformal structures and examine several related topics. In particular, we concentrate on describing the canonical curves and their correspondence. We show that chains and null-chains of an integrable...

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Bibliographic Details
Main Authors: Ma, T, Flood, K. J, Matveev, V. S, Žádník, V
Format: Journal Article
Language:English
Published: 17-06-2023
Subjects:
Mathematics - Analysis of PDEs
Mathematics - Differential Geometry
Mathematics - Representation Theory
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Summary:Nonlinearity 37 (2024), 015007 We present a Fefferman-type construction from Lagrangian contact to conformal structures and examine several related topics. In particular, we concentrate on describing the canonical curves and their correspondence. We show that chains and null-chains of an integrable Lagrangian contact structure are the projections of null-geodesics of the Fefferman space. Employing the Fermat principle, we realize chains as geodesics of Kropina (pseudo-Finsler) metrics. Using recent rigidity results, we show that ``sufficiently many'' chains determine the Lagrangian contact structure. Separately, we comment on Lagrangian contact structures induced by projective structures and the special case of dimension three.
DOI:10.48550/arxiv.2301.09907