Involutive sweeping surfaces with Frenet frame in Euclidean 3-space

In this paper we first define the involutive sweeping surfaces as a new surface form. We then investigate singularity, Gaussian and mean curvatures of these surfaces. By calculating the Gaussian and mean curvatures of the involutive sweeping surfaces, we find necessary conditions of being flat or minimal of these surfaces. Also, we analyze the necessary and sufficient conditions for parameter curves on the surface to be asymptotic, geodesic. Then we investigate the special case that the parameter curves are lines of curvature on the surface. Finally, we illustrate our method of calculation by presenting an example.