CONSTRUCTING SOME NEW FRAMES AND ASSOCIATED CURVES USING THE DARBOUX VECTOR FIELDS OF THE FLC-FRAME

Abstract

In this paper, we define some new frames called the osculating Flc-frame, the normal Flc-frame, and the rectifying Flc-frame along a polynomial space curve using the Darboux vector of the Flc-frame and obtain the derivative equations according to these frames. Also, some new integral curves called the dFlC-direction curve, the Do-direction curve, the Dr-direction curve, and the Dr-direction curve of a polynomial space curve are defined. Later, we give some theorems and results related to these curves.