A generalized second-order frame bundle for Fréchet manifolds

Working within the framework of Fréchet modelled infinite-dimensional manifolds, we propose a generalized notion of second-order frame bundle. We revise in this way the classical notion of bundles of linear frames of order 2, the direct definition and study of which is problematic due to intrinsic difficulties of the space models. However, this new structure keeps all the fundamental characteristics of a frame bundle. It is a principal Fréchet bundle associated (differentially and geometrically) with the corresponding second-order tangent bundle.