Associated Surfaces Obtained Kinematically And Their Projection Areas

Abstract

In this study, we study special two-parameter homothetic motions obtained by the frame of a regular surface with non-umbilical points. This frame has been constructed by taking the unit principal directions and the unit normal vector of the surface. By using the homothetic motion of this frame, we project the orbit surface of a fixed point onto an arbitrary plane and compute its oriented projection area depending on the geodesic curvatures of parameter curves and the principal curvatures of the surface. Also, we reobtain a Holditch-type result for the projection areas.