Holomorphic geometric structures on Hopf manifolds

TL;DR

This paper constructs integrable holomorphic geometric structures on Hopf manifolds and offers a new proof of their normal forms, enhancing understanding of complex geometric structures.

Contribution

It introduces a novel method to build holomorphic G-structures and Cartan geometries on Hopf manifolds without relying on Poincaré-Dulac normal forms.

Findings

Holomorphic G-structures are constructed on all Hopf manifolds.

Flat holomorphic Cartan geometries are established on these manifolds.

A new proof of Poincaré-Dulac normal forms using geometric charts is provided.

Abstract

We construct integrable holomorphic G-structures and flat holomorphic Cartan geometries on every complex Hopf manifold, without using the normal forms given by the Poincar\'e-Dulac Theorem. We provide a new proof of the latter using charts adapted with the geometric structures.