Holomorphic Cartan geometries and Calabi--Yau manifolds

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.)