The rectifying developable and the tangent indicatrix of a curve in Galilean 3-space

Abstract

We study the singularities of Galilean distance and Galilean height functions intrinsically related to Frenet frame along a curve embedded into Galilean space. We establish the relationships between singularities of the functions and geometric invariants under the action of Galilean group of curves which are deeply related to the order of contact with Galilean helices.