Timelike Surface Couple with Bertrand Couple as Joint Geodesic Curves in Minkowski 3-Space
Fatemah Mofarreh
Abstract:A curve on a surface is a geodesic curve if its principal normal vector is anywhere aligned with the surface normal. Using the Serret–Frenet frame, a timelike surface couple (TLSC) with the symmetry of a Bertrand couple (BC) can be specified in terms of linear combinations of the components of the local frames in Minkowski 3-space E13. With these parametric representations, the necessary and sufficient conditions for the specified BC are derived to be the geodesic curves defining these surfaces. Afterward, the… Show more
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