Symmetric Pseudospherical Surfaces I: General Theory

TL;DR

This paper develops a general theoretical framework for analyzing symmetries of pseudospherical surfaces in three-dimensional space using the loop group method, laying the groundwork for future specific case studies.

Contribution

It introduces a comprehensive general theory for symmetries of pseudospherical surfaces employing the loop group method, expanding the mathematical understanding of these surfaces.

Findings

Established a general theoretical approach for pseudospherical surfaces.

Connected the loop group method to symmetry analysis in differential geometry.

Set the stage for detailed case studies in subsequent work.

Abstract

We apply the loop group method developed by Zakharov-Shabat, Terng-Uhlenbeck and Toda to the study of symmetries of pseudospherical surfaces in R^3. In this paper (part I) we consider the general theory, while in a second paper (part II) we will study special cases.