On relation between rational and differential rational invariants of surfaces with respect to the motion groups

Abstract: The description of invariants of surfaces with respect to the motion groups is reduced to the description of invariants of parameterized surfaces with respect to the motion groups. Existence of a commuting system of invariant partial differential operators (derivatives) and a finite system of invariants, such that any invariant of the surface is a function of these invariants and their invariant derivatives, is shown. The offered method is applicable in more general settings than the "Moving Frame Method" does in differential geometry.