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Эта публикация цитируется в 2 научных статьях (всего в 2 статьях)
On the Cauchy–Riemann geometry of transversal curves in the 3-sphere
Emilio Mussoa, Lorenzo Nicolodib, Filippo Salisac a Dipartimento di Matematica, 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
c Istituto Nazionale di Alta Matematica, Italy
Аннотация:
Let $\mathrm S^3$ be the unit sphere of $\mathbb C^2$ with its standard Cauchy–Riemann (CR) structure. This paper investigates the CR geometry of curves in $\mathrm S^3$ which are transversal to the contact distribution, using the local CR invariants of $\mathrm S^3$. More specifically, the focus is on the CR geometry of transversal knots. Four global invariants of transversal knots are considered: the phase anomaly, the CR spin, the Maslov index, and the CR self-linking number. The interplay between these invariants and the Bennequin number of a knot are discussed. Next, the simplest CR invariant variational problem for generic transversal curves is considered and its closed critical curves are studied.
Ключевые слова и фразы:
CR geometry of the 3-sphere, contact geometry, transversal curves, CR invariants of transversal knots, self-linking number, Bennequin number, the strain functional for transversal curves, critical knots.
Поступила в редакцию: 18.03.2020
Образец цитирования:
Emilio Musso, Lorenzo Nicolodi, Filippo Salis, “On the Cauchy–Riemann geometry of transversal curves in the 3-sphere”, Журн. матем. физ., анал., геом., 16:3 (2020), 312–363
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/jmag760 https://www.mathnet.ru/rus/jmag/v16/i3/p312
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