k-Type Hyperbolic Framed Slant Helices in Hyperbolic 3-Space

Abstract

In this paper, we give the existence and uniqueness theorems for hyperbolic framed curves and define the k-type hyperbolic framed slant helices in three-dimensional hyperbolic space. Using the hyperbolic curvature, we investigate the k-type hyperbolic framed slant helices and the connection between them. Hyperbolic framed slant helices might have singular points, they are a generalization of hyperbolic slant helices. Moreover, as their applications, we give some examples of k-type hyperbolic framed slant helices.