FUJIKI CLASS C AND HOLOMORPHIC GEOMETRIC STRUCTURES

Indranil Biswas (1) , Sorin Dumitrescu (2)

1 TIFR - Tata Institute for Fundamental Research
2 LJAD - Laboratoire Jean Alexandre Dieudonné

For holomorphic principal compact torus bundles over Kähler manifolds with vanishing first Chern class, we prove that all holomorphic geometric structures on them, of affine type, are locally homogeneous. For a compact simply connected complex manifold in Fujiki class C, whose dimension is strictly larger than the algebraic dimension, we prove that it does not admit any holomorphic rigid geometric structure, and also it does not admit any holomorphic Cartan geometry of algebraic type. We prove that compact complex simply connected manifolds in Fujiki class C do not admit any holomorphic affine connection.

Domaines: Mathématiques [math]

Indranil Biswas, Sorin Dumitrescu. FUJIKI CLASS C AND HOLOMORPHIC GEOMETRIC STRUCTURES. International Journal of Mathematics, 2020, 31 (5), 17 p. ⟨hal-01803609v2⟩