mKdV-Related Flows for Legendrian Curves in the Pseudohermitian 3-Sphere

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2024
• Main Authors: Calini, Annalisa, Ivey, Thomas, Musso, Emilio
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2024
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212168
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: mKdV-Related Flows for Legendrian Curves in the Pseudohermitian 3-Sphere. Annalisa Calini, Thomas Ivey and Emilio Musso. SIGMA 20 (2024), 027, 30 pages

We investigate geometric evolution equations for Legendrian curves in the 3-sphere, which are invariant under the action of the unitary group U(2). We define a natural symplectic structure on the space of Legendrian loops and show that the modified Korteweg-de Vries equation, along with its associat...