A New Class of Bertrand Curves in Euclidean 4-Space

Abstract

Bertrand curves are a pair of curves that have a common principal normal vector at any point and are related to symmetry properties. In the present paper, we define the notion of 1,3-V Bertrand curves in Euclidean 4-space. Then we find the necessary and sufficient conditions for curves in Euclidean 4-space to be 1,3-V Bertrand curves. Some related examples are given.

Keywords

• Bertrand curves
• curvatures
• Euclidean space