Framed general helix and framed ζ3-slant helix in R4

Abstract

In this paper, we focus on general and zeta(3)-slant helices with any singular points in four-dimensional Euclidean space, which are called framed general and zeta(3)-slant helices, respectively. Then, we state and prove the conditions of necessity and sufficiency for any framed curves to be general helices or zeta(3)-slant helices in R-4. Also, we give some characterizations for framed helices.