  We introduce a geometry on the cone of positive closed currents of bidegree
(p,p) and apply it to define the intersection of such currents. We also
construct and study the Green currents and the equilibrium measure for
horizontal-like mappings. The Green currents satisfy some extremality
properties. The equilibrium measure is invariant, mixing and has maximal
entropy. It is equal to the intersection of the Green currents associated to
the horizontal-like map and to its inverse.
