  In a previous paper, we have introduced a new unified description of the main
equations of the gravitational and of the electromagnetic field, in terms of
tidal tensors and connections on the tangent bundle TM of the space-time
manifold. In the present work, we relate these equations to variational
procedures on the tangent bundle. The Ricci scalar of the proposed connection
is dynamically equivalent to the usual Einstein-Maxwell Lagrangian. Also, in
order to be able to perform these variational procedures, we find an
appropriate completion of the metric tensor (from the base manifold) up to a
metric structure on TM.
