Some properties concerning lifting of Bishop formulas on tangent space T R

Abstract

. In this article, we study the vertical, horizontal and complete lifts of Bishop 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 first and second curvatures κ1 and κ2 of the Bishop formulas according to the vertical, horizontal and complete lifts on space R3 to tangent space T R3 . As a result of this transformation on R3 to tangent space T R3 , it can be speak about the properties of Bishop formulas on space T R3 by looking at the lifting of characteristics (κ1, κ2, T, N1, N2) of the first curve on space R3 .