Connections defined in principal bundles by the action of infinite Lie groups (Q1190923)

For a principal bundle \(P = X\times V\) with an arbitrary connection and of which base \(X\) is diffeomorphic with the manifold of group of a certain Lie group, the author constructs the infinite Lie group \(\Gamma^ H\) of which actions give on \(P\) its geometric structure and shows that the structure equation of the space \(P\) is a necessary condition for the existence of the group \(\Gamma^ H\), giving the considered connection on \(P\).