| MA, Tianyu, Keegan Jonathan FLOOD, Vladimir S MATVEEV and Vojtěch ŽÁDNÍK. Canonical curves and Kropina metrics in Lagrangian contact geometry. Nonlinearity. BRISTOL: IOP Publishing Ltd, 2024, vol. 37, No 1, p. 1-36. ISSN 0951-7715. Available from: 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 and Vojtěch ŽÁDNÍK. Canonical curves and Kropina metrics in Lagrangian contact geometry. \textit{Nonlinearity}. BRISTOL: IOP Publishing Ltd, 2024, vol.~37, No~1, p.~1-36. ISSN~0951-7715. Available from: https://dx.doi.org/10.1088/1361-6544/ad0c2b.
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