On Polynomial Space Curves with Flc-frame

Abstract

The first and second derivatives of a curve provide us fundamental information in the study of the behavior of curve near a point. However, if a curve is a polynomial space curve of degree n, we don’t know what is the geometric meaning of the n-th derivative of the curve? There is no doubt that the Frenet frame is not suitable for this purpose because it is constructed by using first and second derivatives of a curve. On the other hand, in this paper by using a new frame called as Flc-frame we are able to give the geometric meaning of the n-th derivative of a curve. Moreover, we explore some basic concepts regarding polynomial space curves from point of view of Flc-frame in three dimensional Euclidean space.