Integrable Geometric Flows for Curves in the Pseudoconformal 3-Sphere

2019/08/07 by Annalisa Calini, Calini, Annalisa, Thomas Ivey +1
Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1908.02722

openalex publication_date 2019/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider evolution equations for curves in the 3-dimensional sphere S³ that are invariant under the group SU(2,1) of pseudoconformal transformations, which preserves the standard contact structure on the sphere. In particular, we investigate how invariant evolutions of Legendrian and transverse curves induce well-known integrable systems and hierarchies at the level of their geometric invariants.

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