We investigate the total CR twist functional on transversal curves in the standard CR 3-sphere S^3 in 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 speci c class of general critical curves is given. Experimental evidence of the existence of infinite countably many closed critical curves is provided.
On the total twist of transversal curves in the 3-sphere / Musso, Emilio; Nicolodi, Lorenzo. - In: SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS. - ISSN 1815-0659. - 19:(2023), pp. 101.1-101.36. [10.3842/SIGMA.2023.101]
On the total twist of transversal curves in the 3-sphere
Emilio Musso;Lorenzo Nicolodi
2023-01-01
Abstract
We investigate the total CR twist functional on transversal curves in the standard CR 3-sphere S^3 in 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 speci c class of general critical curves is given. Experimental evidence of the existence of infinite countably many closed critical curves is provided.| File | Dimensione | Formato | |
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