Une caract\'erisation des vari\'et\'es complexes compactes parall\'elisables admettant des structures affines

TL;DR

This paper classifies complex compact parallelizable manifolds that admit flat torsion-free holomorphic affine connections and identifies examples that admit affine connections without flat torsion-free ones.

Contribution

It provides a classification of complex compact parallelizable manifolds with specific affine connection properties and highlights the existence of manifolds with certain affine connections but not others.

Findings

Classification of manifolds with flat torsion-free holomorphic affine connections

Examples of manifolds with holomorphic affine connections but no flat torsion-free ones

Insight into the structure of complex compact parallelizable manifolds

Abstract

We classify complex compact parallelizable manifolds which admit flat torsion free holomorphic affine connections. We exhibit complex compact manifolds admitting holomorphic affine connections, but no flat torsion free holomorphic affine connections.