  In Kaluza derived theories the electromagnetic potential is interpreted as a
part of the metric in a higher dimensional theory of gravity. Here we present a
more Yang-Mills like unification of classical electromagnetism and gravity
within five dimensions, where the electromagnetic potential is related to the
connecion and the field strength to the curvature. In addition some aspects of
a quantum theory can be described in the context of the Gauss-Bonnet-Chern
Theorem. This approach offers new coupling mechanisms between gravity and
electromagnetism.
