  In the present article, Chern-Simons gauge theory and its relationship with
gravity are revisited from a geometrical viewpoint. In this setting, our goals
are twofold: In one hand, to show how to represent the family of variational
problems for Chern-Simons theory in the set of $K$-structures on the space-time
$M$, by means of a unique variational problem of Griffiths type. On the other
hand, to make an interpretation of the correspondence of these theories in
terms of the correspondence between the frame bundle and its affine
counterpart.
