  In this paper, we define the semi-symmetric metric connection on the algebra
of differential forms. We compute some special semi-symmetric metric
connections and their curvature tensor and their Ricci tensor on the algebra of
differential forms. We study the distribution on the algebra of differential
forms and we get its Gauss-Codazzi-Ricci equations associated to the
semi-symmetric metric connection. We also study the Lie derivative of the
distribution on the algebra of differential forms. We define the canonical
connection and the Schouten connection and the Vrancreanu connection on the
algebra of differential forms and get some properties of these connections.
