Exotic geometric structures on Kodaira surfaces

TL;DR

This paper classifies all locally homogeneous geometric structures on compact complex surfaces, focusing on those isomorphic to exotic homogeneous surfaces of Lie, providing a comprehensive understanding of their geometric configurations.

Contribution

It offers a complete classification of exotic geometric structures on Kodaira surfaces, expanding the understanding of complex surface geometries.

Findings

Classification of all locally homogeneous structures on Kodaira surfaces

Identification of exotic homogeneous surfaces of Lie in this context

Extension of geometric structure theory on complex surfaces

Abstract

On all compact complex surfaces (modulo finite unramified coverings), we classify all of the locally homogeneous geometric structures which are locally isomorphic to the exotic homogeneous surfaces of Lie.