The Hyperbolic Darboux Image And The Rectifying Gaussian Surface Of A Nonlightlike Curve In Minkowski 3-Space

In this paper we give the classifications of the singularities of the hyperbolic Dar-boux imaged and the rectifying Gaussian surface of a nonlightlike curve in Minkowski 3-space. Moreover we establish the relationships between singularities of these subjects and geometric invariants of curves which are deeply related to the order of contact with helices.We struct two different families of smooth functions on a curve which are useful for the study of singularities of the hyperbolic Darboux imaged and the rectifying Gaussian surface : binormal directed height functions and functions depending on binormal directed height functions.Thus singularity theorem is used to study the classifications of singularities of hyperbolic Darboux image and the rectifying Gaussian surface.