Equivariant bundles and adapted connections

摘要

Given a complex manifold M equipped with a holomorphic action of a connected complexLie group G, and a holomorphic principal H-bundle EH over X equipped with a G-connection h, we investigate the connections on the principal H-bundle EH that are (strongly) adapted to h. Examples are provided by holomorphic principal H-bundles equipped with a flat partial connection over a foliated manifold.