# Integrable Geometric Flows for Curves in the Pseudoconformal 3-Sphere

## TL;DR

This paper explores how invariant geometric flows of curves in the pseudoconformal 3-sphere relate to integrable systems, revealing new connections between geometry and integrability.

## Contribution

It introduces integrable geometric flows for curves in the pseudoconformal 3-sphere and links these flows to known integrable systems through their invariants.

## Key findings

- Invariant curve evolutions induce well-known integrable hierarchies.
- The work connects geometric invariants with integrable PDEs.
- Provides a geometric framework for understanding integrability in contact geometry.

## Abstract

We consider evolution equations for curves in the 3-dimensional sphere $S^3$ 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.