Framed general helix and framed ζ3-slant helix in ℝ4

Abstract

In this paper, we focus on general and ζ3-slant helices with any singular points in four-dimensional Euclidean space, which are called framed general and ζ3-slant helices, respectively. Then, we state and prove the conditions of necessity and su ciency for any framed curves to be general helices or ζ3-slant helices in ℝ4. Also, we give some characterizations for framed helices.

Keywords

• framed curve
• general helix
• slant helix
• 53a04
• 57r45
• 58k05