Killing vector fields for some meromorphic affine connections

Champs de Killing pour certaines connexions affines méromorphes

Alexis Garcia (1)

1 LJAD - Laboratoire Jean Alexandre Dieudonné

We give a geometric assumption on a meromorphic affine connection for its Killing vector fields to be univaluated. For, we prove a general result on the infinitesimal automorphisms for a subcategory of meromorphic Cartan geometries, and uses the equivalence with the former geometric structures. This result is applied to the classification on complex compact manifolds with algebraic dimension zero, extending partially the main result of [3].

Domaines: Géométrie différentielle [math.DG]; Variables complexes [math.CV]

Alexis Garcia. Killing vector fields for some meromorphic affine connections. 2022. ⟨hal-03680548v4⟩