THE NATURAL LIFT CURVES AND GEODESIC CURVATURES OF THE SPHERICAL INDICATRICES OF THE TIMELIKE BERTRAND CURVE COUPLE

Abstract

In this paper, when (alpha, alpha*) timelike Bertrand curve couple is given, the geodesic curves and the arc-lenghts of the curvatures (T*), (N*), (B*) and the fixed pole curve (C*) which are generated over the S(1)(2)Lorentz sphere or the H O(2)hyperbolic sphere by the Frenet vectors {T*, N*, B* } and the unit Darboux vector C* have been obtained. The condition being the naturel lifts of the spherical indicatrix of the alpha* is an integral curve of the geodesic spray has expressed.