Canonical curves and Kropina metrics in Lagrangian contact geometry

• Autoři: MA Tianyu; FLOOD Keegan Jonathan; MATVEEV Vladimir S; ŽÁDNÍK Vojtěch
• Rok publikování: 2024
• Druh: Článek v odborném periodiku
• Časopis / Zdroj: Nonlinearity
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• www: https://iopscience.iop.org/article/10.1088/1361-6544/ad0c2b
• Doi: http://dx.doi.org/10.1088/1361-6544/ad0c2b
• Klíčová slova: Fefferman-type construction; Lagrangian contact structure; chains; Kropina metric; pseudo-Finsler metric; null geodesics
• Popis: 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.

Související projekty

• Symetrie a invariance v analýze, geometrickém modelování a teorii optimálního řízení
• Variacizace význačných křivek v Cartanově geometrii