New-Type Tangent Indicatrix of Involute and Ruled Surface According to Blaschke Frame in Dual Space

Abstract

In this study we first take the tangent vector of an involute curve in dual space as a generating vector and define the dual Blaschke frame and Blaschke invariants of a new type of tangent indicatrix of the involute curve. We then introduce the ruled surfaces generated by the dual Blashke frame using Study's transfer principle and compute the geometric invariants of these surfaces, thus obtaining some important results about them. We illustrate our method by presenting an example.