(TE)-structures over the irreducible 2-dimensional globally nilpotent F-manifold germ

TL;DR

This paper classifies and normalizes certain meromorphic connections called (TE)-structures over a specific 2-dimensional nilpotent F-manifold, providing a detailed understanding of their forms and the Euler fields they induce.

Contribution

It introduces formal and holomorphic normal forms for (TE)-structures over the irreducible 2D globally nilpotent F-manifold germ and characterizes the Euler fields associated with these structures.

Findings

Normal forms for (TE)-structures over the manifold germ.

Characterization of Euler fields induced by (TE)-structures.

Identification of conditions for Euler fields on the manifold.

Abstract

We find formal and holomorphic normal forms for a class of meromorphic connections (the so-called $(TE)$-structures) over the irreducible $2$-dimensional globally nilpotent $F$-manifold germ $\mathcal N_{2}$. We find normal forms for Euler fields on $\mathcal N_{2}$ and we characterize the Euler fields on $\mathcal N_{2}$ which are induced by a $(TE)$-structure.