Smarandache curves in Euclidean 4- space E4

Abstract

The purpose of this paper is to study Smarandache curves in the 4-dimensional Euclidean space E4, and to obtain the Frenet–Serret and Bishop invariants for the Smarandache curves in E4. The first, the second and the third curvatures of Smarandache curves are calculated. These values depending upon the first, the second and the third curvature of the given curve.

Keywords

• Euclidean 4- space
• Smarandache curves
• Ferent frame
• Parallel transport frame