In this ticket, I'd like to introduce vector valued forms with values in a vector bundle by using a generalization of the class sage.tensor.modules.comp.Components allowing its element to be more general elements (in this case differential forms). In a next step, a bundle connection is introduced having these components as coefficients (see: connection matrix).

This is also useful for characteristic class on vector bundles and a corresponding embedding is easily handled.

Since I am really short of time, I'm afraid this ticket have to wait.

CC: @egourgoulhon

Component: geometry

Author: Michael Jung

Issue created by migration from https://trac.sagemath.org/ticket/28640