  We address the equations of motion for the light-like QCD Wilson exponentials
defined in the generalized loop space. We attribute an important class of the
infinitesimal shape variations of the rectangular light-like Wilson loops to
the Fr\'echet derivative associated to a diffeomorphism in loop space what
enables the derivation of the law of the classically conformal-invariant shape
variations. We show explicitly that the Fr\'echet derivative coincides (at
least in the leading perturbative or- der) with the area differential operator
introduced in the previous works. We discuss interesting implications of this
result which will allow one to relate the rapidity evolution and ultra-violet
evolution of phenomenologically important quantum correlation functions (such
as 3-dimensional parton distribution functions) and geometrical properties of
the light-like cusped Wilson loops.
