Recursion Operators and Frobenius Manifolds

TL;DR

This paper explores the connections between F-manifolds, Frobenius manifolds, and Poisson-Nijenhuis manifolds through a novel discrete homotopy, revealing new relationships in geometric structures.

Contribution

It introduces a discrete homotopy linking F-manifolds, Frobenius manifolds, and Poisson-Nijenhuis manifolds, providing a new perspective on their interrelations.

Findings

Established a discrete homotopy connecting the categories

Linked F-manifolds to Frobenius and Poisson-Nijenhuis manifolds

Revealed new geometric relationships among these structures

Abstract

In this note I exhibit a "discrete homotopy" which joins the category of F-manifolds to the category of Poisson-Nijenhuis manifolds, passing through the category of Frobenius manifolds.