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

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 N2. We find normal forms for Euler fields on N2 and we characterize the Euler fields on N2 which are induced by a (TE)-structure.