Canonical curves and Kropina metrics in Lagrangian contact
geometry

J 2024

Canonical curves and Kropina metrics in Lagrangian contact geometry

MA, Tianyu, Keegan Jonathan FLOOD, Vladimir S MATVEEV and Vojtěch ŽÁDNÍK

Basic information

Original name

Canonical curves and Kropina metrics in Lagrangian contact geometry

Authors

MA, Tianyu, Keegan Jonathan FLOOD (840 United States of America, belonging to the institution), Vladimir S MATVEEV and Vojtěch ŽÁDNÍK (203 Czech Republic, guarantor, belonging to the institution)

Edition

Nonlinearity, BRISTOL, IOP Publishing Ltd, 2024, 0951-7715

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

Netherlands

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Impact factor

Impact factor: 1.700 in 2022

Organization unit

Faculty of Science

DOI

http://dx.doi.org/10.1088/1361-6544/ad0c2b

UT WoS

001118895700001

Keywords in English

Fefferman-type construction; Lagrangian contact structure; chains; Kropina metric; pseudo-Finsler metric; null geodesics

Abstract

V originále

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.

Links

GA20-11473S, research and development project

Name: Symetrie a invariance v analýze, geometrickém modelování a teorii optimálního řízení

Investor: Czech Science Foundation

8J20DE004, research and development project

Name: Variacizace význačných křivek v Cartanově geometrii (Acronym: VVKCG)

Investor: Ministry of Education, Youth and Sports of the CR, Germany

Citovat

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.

@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.

Detailed Information on Publication Record