Some Properties on Lifting of Frenet Formulas on Tangent Space T R

Abstract

In this paper, we study the vertical, horizontal and complete lifts of Frenet formulas given by ( 1. 1 ), the first acceleration pool centers and the Darboux vector defined on space R3 to its tangent space T R3 = R6 . In addition, we include all special cases of the curvature κ and torsion τ0 of the Frenet formulas with respect to the vertical, horizontal and complete lifts on space R3 to its tangent space T R3 . As a result of this transformation on space R3 to its tangent space T R3 , we can speak about the features of Frenet formulas on space T R3 by looking at the lifting of characteristics {T, N, B, κ, τ0} of the first curve on space R3 . Each curve transformation supported by examples.