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We present a Fefferman-type construction from Lagrangian contact to conformalstructures and examine several related topics. In particular, we concentrate ondescribing the canonical curves and their correspondence. We show that chainsand null-chains of an integrable Lagrangian contact structure are theprojections of null-geodesics of the Fefferman space. Employing the Fermatprinciple, we realize chains as geodesics of Kropina (pseudo-Finsler) metrics.Using recent rigidity results, we show that ``sufficiently many'' chainsdetermine the Lagrangian contact structure. Separately, we comment onLagrangian contact structures induced by projective structures and the specialcase of dimension three.

Canonical curves and Kropina metrics in Lagrangian contact geometry