NOTES ON LIFTING OF BERTRAND CURVE ON TANGENT SPACE TR3

HASIM CEAYIR, FIDAN JABRAILZADE
2018 Poincare journal of analysis and applications  
In this paper, firstly, we define the Bertrand curve of any curve with respect to the vertical, complete and horizontal lifts on space R 3 to its tangent space T R 3 = R 6 . Secondly, we examine the Frenet-Serret aparatus } and the Darboux vector W * of the Bertrand curve α * according to the vertical, complete and horizontal lifts on T R 3 by depend on the lifting of Frenet-Serret aparatus {T (s), N (s), B(s), κ, τ } of the first curve α on space R 3 . As a result of this transformation on
more » ... ansformation on space R 3 to its tangent space T R 3 , we can speak about the features of Bertrand curve of any curve on space T R 3 by looking at the characteristics of the first curve.
doi:10.46753/pjaa.2018.v05i02(i).002 fatcat:glk76lkrznej5poejme6vtof3m