Darboux Frame of a Curve Lying on a Lightlike Surface

Abstract

In this study, the Darboux frame is given for a curve lying on the lightlike surface of three dimensional Minkowski space. Moreover, known curvatures of the curve are obtained according to the Darboux frame and relationships between these curvatures are acquired. In specific case, by taking into consideration that the surface is a lightlike cone, similar characterizations are investigated.