Abstract:
In the differential geometry of curves and surfaces, the curvatures of curves and surfaces are often calculated
and results are given. In particular, the results given by using the apparatus of the curve-surface pair are
important in terms of what kind of surface the surface indicates. In this study, some relationships between
curvatures of the parallel surface pair (X;Xr) via structure functions of non-developable ruled surface
X(u; v) = a(u) + vb(u) are established such that a(u) is striction curve of non-developable surface and
b(u) is a unit spherical curve in E3. Especially, it is examined whether the non-developable surface Xr is
minimal surface, linear Weingarten surface and Weingarten surface. X and its parallel Xr are expressed
on the Helicoid surface sample. It is indicated on the figure with the help of SWP. Moreover, curvatures of
curve-surface pairs (X; a) and (Xr; ) are investigated and some conclusions are obtained.