The search for solitons on homogeneous spaces

TL;DR

This paper explores the concept of solitons on homogeneous spaces, highlighting their role in identifying canonical geometric structures across various geometries such as Riemannian, pseudo-Riemannian, complex, symplectic, and G2.

Contribution

It generalizes the notion of solitons to homogeneous spaces and demonstrates their utility in finding distinguished geometric structures in diverse geometric contexts.

Findings

Solitons serve as canonical elements in various geometric settings.

Homogeneous spaces provide a natural framework for soliton analysis.

The approach unifies different geometric structures under the soliton concept.

Abstract

The concept of soliton, in its most general version, allows us to find canonical or distinguished elements on any set provided with an equivalence relation and an `optimal' tangent direction at each point. We study in this paper solitons on homogeneous spaces, which have consolidated its role as a quite useful tool to find soliton geometric structures in Riemannian, pseudo-Riemannian, complex, symplectic and G2 geometries.