Haantjes manifolds with symmetry

TL;DR

This paper introduces Haantjes manifolds with symmetry and explains their relevance in integrable hydrodynamic systems and topological field theories, highlighting their theoretical significance.

Contribution

It defines Haantjes manifolds with symmetry and clarifies their role in the context of integrable systems and topological field theories.

Findings

Haantjes manifolds with symmetry are formally defined.

These manifolds are shown to appear naturally in integrable hydrodynamic systems.

They also have applications in topological field theories.

Abstract

This paper has two purposes. The first is to introduce the definition of Haantjes manifolds with symmetry. The second is to explain why these manifolds appear in the theory of integrable systems of hydrodynamic type and in topological field theories.