Characterizations of Normal and Binormal Surfaces in G3

Abstract

In this paper, our aim is to give surfaces in the Galilean 3-space G3 with the property that there exist four geodesics through each point such that every surface built with the normal lines and the binormal lines along these geodesics is a surface with a minimal surface and a constant negative Gaussian curvature. We show that $\psi $ should be an isoparametric surface in G3: A plane or a circular hyperboloid.