On the Cauchy - Riemann Geometry of Transversal Curves in the 3-Sphere


  • Emilio Musso Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy
  • Lorenzo Nicolodi Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma, Parco Area delle Scienze 53/A, I-43124 Parma, Italy
  • Filippo Salis Istituto Nazionale di Alta Matematica, Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy



Ключові слова:

CR геометрія тривимірної сфери, контактна геометрія, трансверсальні криві, CR інваріанти трансверсальних вузлів, число самозацеплення, число Беннеквіна, деформація функціоналу для трансверсальних кривих, критичні вузли


Нехай $S^3$ є одиничною сферою у $\mathbb{C}^2$ зі стандартною структурою Коші-Рімана (CR). Використовуючи локальні CR інваріанти $S^3$, у цій статті досліджено CR геометрію кривих в $S^3$, які трансверсальні до контактного розподілу. А саме, у центрі уваги є CR геометрія трансверсальних вузлів. Розглянуто чотири глобальні інваріанти трансверсальних вузлів: фазова аномалія, CR спін, індекс Маслова та CR число самозацеплення. Обговорюється зв’язок між цими інваріантами і числом Беннеквіна вузла. Також розглянуто найпростішу CR інваріантну варіаційну проблему для загальних трансверсальних кривих і досліджено замкнуті критичні криві.

Mathematics Subject Classification: 53C50, 53C42, 53A10


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Як цитувати

Musso, E.; Nicolodi, L.; Salis, F. On the Cauchy - Riemann Geometry of Transversal Curves in the 3-Sphere. Журн. мат. фіз. анал. геом. 2020, 16, 312-363.





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