MA, Tianyu, Keegan Jonathan FLOOD, Vladimir S MATVEEV a Vojtěch ŽÁDNÍK. Canonical curves and Kropina metrics in Lagrangian contact geometry. Nonlinearity. BRISTOL: IOP Publishing Ltd, 2024, roč. 37, č. 1, s. 1-36. ISSN 0951-7715. Dostupné z: https://dx.doi.org/10.1088/1361-6544/ad0c2b. |
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@article{2368015, author = {Ma, Tianyu and Flood, Keegan Jonathan and Matveev, Vladimir S and Žádník, Vojtěch}, article_location = {BRISTOL}, article_number = {1}, doi = {http://dx.doi.org/10.1088/1361-6544/ad0c2b}, keywords = {Fefferman-type construction; Lagrangian contact structure; chains; Kropina metric; pseudo-Finsler metric; null geodesics}, language = {eng}, issn = {0951-7715}, journal = {Nonlinearity}, title = {Canonical curves and Kropina metrics in Lagrangian contact geometry}, url = {https://iopscience.iop.org/article/10.1088/1361-6544/ad0c2b}, volume = {37}, year = {2024} }
TY - JOUR ID - 2368015 AU - Ma, Tianyu - Flood, Keegan Jonathan - Matveev, Vladimir S - Žádník, Vojtěch PY - 2024 TI - Canonical curves and Kropina metrics in Lagrangian contact geometry JF - Nonlinearity VL - 37 IS - 1 SP - 1-36 EP - 1-36 PB - IOP Publishing Ltd SN - 09517715 KW - Fefferman-type construction KW - Lagrangian contact structure KW - chains KW - Kropina metric KW - pseudo-Finsler metric KW - null geodesics UR - https://iopscience.iop.org/article/10.1088/1361-6544/ad0c2b N2 - 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. ER -
MA, Tianyu, Keegan Jonathan FLOOD, Vladimir S MATVEEV a Vojtěch ŽÁDNÍK. Canonical curves and Kropina metrics in Lagrangian contact geometry. \textit{Nonlinearity}. BRISTOL: IOP Publishing Ltd, 2024, roč.~37, č.~1, s.~1-36. ISSN~0951-7715. Dostupné z: https://dx.doi.org/10.1088/1361-6544/ad0c2b.
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