  Motivated by a number of recent investigations, we define and investigate the
various properties of the ruled surfaces depend on three dimensional Lie groups
with a bi-variant metric. We give useful results involving the
characterizations of these ruled surfaces. Some special ruled surfaces such as
normal surface, binormal surface, tangent developable surface, rectifying
developable surface and Darboux developable surface are worked. From those
applications, we make use of such a work to interpret the Gaussian, mean
curvatures of these surfaces and geodesic, normal curvature and geodesic
torsion of the base curves with respect to these surfaces depend on three
dimensional Lie groups.
