Semi-geodetic coordinate nets through isometries

Every coordinate net on a rotating surface is a semi-geodesic coordinate net composed of a family of curves of constant geodesic curvature. In this paper, using semi-geodesic coordinate nets on special rotating surfaces such as a conical surface, a catenoid, and a rotational hyperboloid surface, we give families of curves of constant geodesic curvature on some surfaces through isometric mappings. Also, with the aid of the software Mathematica, we draw images of the semi-geodesic coordinate nets and the family of curves obtained through isometric mappings.