Ac-Slant Curves in Euclidean 3-Space

Abstract

In this study, we introduce a new type of space curve which is called ac-slant curve whose inner product of its acceleration vector and a fixed direction is a constant. Then, we give a characterization according to the curvatures of ac-slant curve. Later on, we obtain relationship between an ac-slant curve and some special curves (spherical curve, helix, slant helix, Salkowski curve, rectifying curve). Similarly to concept of ac-slant curves, we consider normalized ac-slant curve which has a unit acceleration vector and give a characterization with respect to its curvatures. Especially, we give some results for ac-slant or normalized ac-slant curves with respect to the magnitude of its velocity and acceleration vector.