Geodesic
On the Total CR Twist of Transversal Curves in the $3$-Sphere
Symmetry, integrability and geometry: methods and applications, Tome 19 (2023) Cet article a éte moissonné depuis la source Math-Net.Ru

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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, total CR twist, Griffiths' formalism, integration by quadratures, closed critical curves.
Mots-clés : transversal curves, CR invariants, Lax formulation of E-L equations 
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     author = {Emilio Musso and Lorenzo Nicolodi},
     title = {On the {Total} {CR} {Twist} of {Transversal} {Curves} in the $3${-Sphere}},
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     year = {2023},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2023_19_a100/}
}
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Emilio Musso; Lorenzo Nicolodi. On the Total CR Twist of Transversal Curves in the $3$-Sphere. Symmetry, integrability and geometry: methods and applications, Tome 19 (2023). http://geodesic.mathdoc.fr/item/SIGMA_2023_19_a100/

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