Integrable Geometric Flows for Curves in Pseudoconformal S3

Abstract We consider evolution equations for curves in the 3-dimensional sphere S 3 that are invariant under the group S U ( 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 both new and well-known integrable systems and hierarchies at the level of their geometric invariants.