Killing vector fields for some meromorphic affine connections

Abstract

AbstractWe give a geometric condition on a meromorphic affine connection for its Killing vector fields to be single valued. More precisely, this condition relies on the pole of the connection and its geodesics, and defines a subcategory. To this end, we use the equivalence between these objects and meromorphic affine Cartan geometries. The proof of the previous result is then a consequence of a more general result linking the distinguished curves of meromorphic Cartan geometries, their poles and their infinitesimal automorphisms. This enables to extend the result of [1] to the subcategory of meromorphic affine connection described before. 2010 MSC Classification: 53B21, 53C56, 53A55