Isometric Immersions of Space Forms and Soliton Theory

TL;DR

This paper explores the use of integrable systems and Lax pairs to study isometric immersions of space forms, connecting differential geometry with soliton theory.

Contribution

It introduces a hierarchy of finite-dimensional integrable systems in Lax form to analyze isometric immersions of space forms, bridging geometry and soliton theory.

Findings

Established a new integrable systems framework for space form immersions

Connected differential geometry with soliton theory techniques

Provided insights into the structure of isometric immersions

Abstract

This paper studies isometric immersions of space forms by means of a hierarchy of finite dimensional integrable systems in Lax form on loop algebras.