Holomorphic Cartan geometries and Calabi-Yau manifolds (Q962052)

The present paper deals with a conjecture of the second author concerning Calabi-Yau manifolds. Namely, in a submitted paper he conjectured that if \(M\) is a Calabi-Yau manifold admitting a holomorphic Cartan geometry, then \(M\) is holomorphically covered by a complex torus. The authors prove that the conjecture holds under the assumption that \(M\) is complex projective. More precisely, they prove the following theorem: Any Calabi-Yau complex projective manifold \(M\) bearing a holomorphic Cartan geometry is holomorphically covered by an abelian variety. Notice that, however, more recently the conjecture has been completely proved by the authors [Differ. Geom. Appl. 28, No.~1, 102--106 (2010; Zbl 1187.53028)].