Canonical curves and Kropina metrics in Lagrangian contact geometry
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Published:2023-12-05
Issue:1
Volume:37
Page:015007
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ISSN:0951-7715
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Container-title:Nonlinearity
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language:
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Short-container-title:Nonlinearity
Author:
Ma Tianyu,
Flood Keegan J,
Matveev Vladimir SORCID,
Žádník Vojtěch
Abstract
Abstract
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.
Funder
Deutscher Akademischer Austauschdienst
Ministerstvo Školství, Mládeže a Tělovýchovy
Grantová Agentura České Republiky
Deutsche Forschungsgemeinschaft
Subject
Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics
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