Let S^3 be the unit 3-sphere with its standard Cauchy--Riemann (CR) structure induced from C^2. This paper investigates the CR geometry of curves in S^3 transversal to the contact distribution using the local CR invariants of S^3 thought of as a 3-dimensional CR manifold. More specifically, the focus is on the CR geometry of transversal knots in the 3-sphere. Four global invariants of transversal knots are considered: the phase anomaly, the pseudoconformal spin, the Maslov index, and the Cauchy--Riemann self-linking number. The relations between these invariants and the Bennequin number of a knot are discussed. Next, the simplest CR invariant variational problem for generic transversal curves, the CR strain functional, is considered and its closed critical curves are studied.
On the Cauchy-Riemann Geometry of Transversal Curves in the 3-Sphere / Musso, Emilio; Nicolodi, Lorenzo; Filippo Salis, And. - In: ŽURNAL MATEMATIčESKOJ FIZIKI, ANALIZA, GEOMETRII. - ISSN 1812-9471. - ELETTRONICO. - 16:3(2020), pp. 312-363.
Titolo: | On the Cauchy-Riemann Geometry of Transversal Curves in the 3-Sphere |
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Data di pubblicazione: | 2020 |
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Appare nelle tipologie: | 1.1 Articolo in rivista |
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http://hdl.handle.net/11583/2849192