B\"acklund transformations for transparent connections

TL;DR

This paper characterizes all transparent SU(2)-connections on negatively curved surfaces and demonstrates they can be constructed using Bäcklund transformations, advancing understanding of geometric structures related to integrable systems.

Contribution

It provides a complete classification of transparent SU(2)-connections on negatively curved surfaces and introduces a method to generate them via Bäcklund transformations.

Findings

All transparent SU(2)-connections are classified.

Transparent connections can be constructed from Bäcklund transformations.

The approach links geometric analysis with integrable systems theory.

Abstract

Let $M$ be a closed orientable surface of negative curvature. A connection is said to be transparent if its parallel transport along closed geodesics is the identity. We describe all transparent SU(2)-connections and we show that they can be built up from suitable B\"acklund transformations.