Holomorphic Cartan geometries and Calabi--Yau manifolds

TL;DR

This paper proves that among Calabi--Yau projective manifolds, only abelian varieties admit holomorphic Cartan geometries, highlighting a unique geometric property of abelian varieties within Calabi--Yau manifolds.

Contribution

It establishes a classification result showing that holomorphic Cartan geometries are exclusive to abelian varieties among Calabi--Yau projective manifolds.

Findings

Only abelian varieties admit holomorphic Cartan geometries among Calabi--Yau projective manifolds.

Provides a classification linking Cartan geometries to the structure of Calabi--Yau manifolds.

Enhances understanding of geometric structures on Calabi--Yau manifolds.

Abstract

We prove that the only Calabi--Yau projective manifolds which bear holomorphic Cartan geometries are precisely the abelian varieties. (Nous d\'emontrons que les seules vari\'et\'es projectives de Calabi--Yau qui poss\`edent des g\'eom\'etrie holomorphes de Cartan sont les vari\'et\'es ab\'eliennes.)