Timelike surfaces with Bertrand geodesic curves in Minkowski 3–space

Abstract

Geodesic curves on a surface play an essential role in reasonable implementation. A curve on a surface is a geodesic curve if its principal normal vector is aligned with the surface normal. Using the Serret–Frenet frame, the timelike (TL) surfaces can be specified as linear combinations of the components of the local frames in Minkowski 3–space E13. With these parametric representations, we obtained the indispensable and required events for the specified Bertrand (B) curves to be the geodesic curves on these surfaces. Afterword, the conclusion regarding the TL ruled surface is also made. Finally, the models are declared to assure that the suggested methods are effective in outcome manufacturing by modifying the styles of the surface pair.