On the Quaternionic Normal Curves in the Euclidean Space

Abstract

In this paper, we define the quaternionic normal curves in Euclidean 3-space E^3 and Euclidean 4-space E^4. We obtain some characterizations of quaternionic normal curves in terms of their curvature functions. Moreover, we give necessary and sufficient condition for a quaternionic curves to be quaternionic normal curves in E^3 and E^4 respectively.