Locally homogeneous structures on Hopf surfaces

TL;DR

This paper classifies holomorphic locally homogeneous geometric structures modeled on line bundles over the projective line on primary Hopf surfaces, providing explicit descriptions of their developing maps and holonomy morphisms.

Contribution

It offers a complete classification and explicit descriptions of such structures on primary Hopf surfaces, advancing understanding of their geometric properties.

Findings

Classification of locally homogeneous structures on primary Hopf surfaces

Explicit formulas for developing maps and holonomy morphisms

Identification of geometric structures modeled on line bundles over the projective line

Abstract

We study holomorphic locally homogeneous geometric structures modelled on line bundles over the projective line. We classify these structures on primary Hopf surfaces. We write out the developing map and holonomy morphism of each of these structures explicitly on each primary Hopf surface.