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.
