HOLOMORPHIC AFFINE CONNECTIONS ON NON-KÄHLER MANIFOLDS

Indranil Biswas (1) , Sorin Dumitrescu (2)

1 Algebraic geometry
2 LJAD - Laboratoire Jean Alexandre Dieudonné

Our aim here is to investigate the holomorphic geometric structures on compact complex manifolds which may not be Kähler. We prove that holomorphic geometric structures of affine type on compact Calabi-Yau manifolds with polystable tangent bundle (with respect to some Gauduchon metric on it) are locally homogeneous. In particular, if the geometric structure is rigid in Gromov's sense, then the fundamental group of the manifold must be infinite. We also prove that compact complex manifolds of algebraic dimension one bearing a holomorphic Riemannian metric must have infinite fundamental group.

Mots clés: holomorphic geometric structures; Calabi-Yau manifolds

Domaines: Mathématiques [math]

Indranil Biswas, Sorin Dumitrescu. HOLOMORPHIC AFFINE CONNECTIONS ON NON-KÄHLER MANIFOLDS. International Journal of Mathematics, 2016, International Journal of Mathematics, 27 (11). ⟨hal-01274412⟩