Partner Curves in Three Dimensional Degenerated Space Form

Abstract

Using elementary and effective methods we study cone curves and their associated curves or partner curves in the three dimensional lightlike cone $\Q^3$, which is called three dimensional degenerated space form of the four dimensional Minkowski space $\E^4_1$. We define the associated curve of the cone curve and also partner curves of some special curves, such as a Bertrand curve and a Mannheim curve. We consider the properties and relations of a curve and its associated curve or partner curve. Some geometric characterizations of these curves are also given.