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Symmetry, Integrability and Geometry: Methods and Applications, 2023, Volume 19, 101, 36 pp.
DOI: https://doi.org/10.3842/SIGMA.2023.101 (Mi sigma1996) 		 
On the Total CR Twist of Transversal Curves in the $3$-Sphere

Emilio Mussoa, Lorenzo Nicolodib

a Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy
b Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma, Parco Area delle Scienze 53/A, I-43124 Parma, Italy
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DOI: https://doi.org/10.3842/SIGMA.2023.101
Abstract: We investigate the total CR twist functional on transversal curves in the standard CR $3$-sphere $\mathrm S^3 \subset \mathbb C^2$. The question of the integration by quadratures of the critical curves and the problem of existence and properties of closed critical curves are addressed. A procedure for the explicit integration of general critical curves is provided and a characterization of closed curves within a specific class of general critical curves is given. Experimental evidence of the existence of infinite countably many closed critical curves is provided.
Keywords: CR $3$-sphere, transversal curves, CR invariants, total CR twist, Griffiths' formalism, Lax formulation of E-L equations, integration by quadratures, closed critical curves.
Funding agency Grant number
Istituto Nazionale di Alta Matematica "Francesco Severi"
Italian Ministry of Education, University and Research E11G18000350001
The authors were partially supported by PRIN 2017 “Real and Complex Manifolds: Topology, Geometry and holomorphic dynamics” (protocollo 2017JZ2SW5-004); and by the GNSAGA of INdAM. The present research was also partially supported by MIUR grant “Dipartimenti di Eccellenza” 2018-2022, CUP: E11G18000350001, DISMA, Politecnico di Torino.
Received: July 11, 2023; in final form November 26, 2023; Published online December 21, 2023
Document Type: Article
MSC: 53C50, 53C42, 53A10
Language: English
Citation: Emilio Musso, Lorenzo Nicolodi, “On the Total CR Twist of Transversal Curves in the $3$-Sphere”, SIGMA, 19 (2023), 101, 36 pp.
Citation in format AMSBIB
\Bibitem{MusNic23}
\by Emilio~Musso, Lorenzo~Nicolodi
\paper On the Total CR Twist of Transversal Curves in the $3$-Sphere
\jour SIGMA
\yr 2023
\vol 19
\papernumber 101
\totalpages 36
\mathnet{http://mi.mathnet.ru/sigma1996}
\crossref{https://doi.org/10.3842/SIGMA.2023.101}
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