Holomorphic G-structures and foliated Cartan geometries on compact complex manifolds

TL;DR

This survey explores holomorphic G-structures and Cartan geometries on compact complex manifolds, focusing on foliated cases with transverse holomorphic geometries, highlighting recent developments and classifications.

Contribution

It provides a comprehensive overview of foliated holomorphic Cartan geometries on compact complex manifolds, emphasizing the transverse structures and their classifications.

Findings

Classification results for foliated Cartan geometries

Examples of holomorphic G-structures on compact manifolds

Connections between foliations and holomorphic geometries

Abstract

This is a survey paper dealing with holomorphic G-structures and holomorphic Cartan geometries on compact complex manifolds. Our emphasis is on the foliated case: holomorphic foliations with transverse (branched or generalized) holomorphic Cartan geometries.