A new study on focal surface of a given surface

Abstract

Focal surfaces are special cases of line congruences. With the aid of the definiton of a focal surface of a given surface M, we obtain a new type of focal surface in Galilean 3-space G_3. We show that the focal surface we found is not the same type of surface as the given surface. We present the visualizations of the focal surface and the given surface with an example. Lastly, by searching the curvature functions, we give the minimality conditions of the focal surface.