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 in nite 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 in nite countably many closed critical curves is provided.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
