Canonical curves and Kropina metrics in Lagrangian contact geometry

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MA Tianyu FLOOD Keegan Jonathan MATVEEV Vladimir S ŽÁDNÍK Vojtěch

Year of publication 2024
Type Article in Periodical
Magazine / Source Nonlinearity
MU Faculty or unit

Faculty of Science

Keywords Fefferman-type construction; Lagrangian contact structure; chains; Kropina metric; pseudo-Finsler metric; null geodesics
Description We present a Fefferman-type construction from Lagrangian contact to split-signature conformal structures and examine several related topics. In particular, we describe 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.
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