Generalized Bertrand curves with timelike (1,3)-normal plane in Minkowski space-time

Abstract

In this paper, we reconsider the (1,3)-Bertrand curves with respect to the casualcharacters of (1,3)-normal plane which is a plane spanned by the principal normal andthe second binormal vector fields of the given curve. Here, we restrict our investigationof (1,3)-Bertrand curves to the timelike (1,3)-normal plane in Minkowski spacetime.We obtain the necessary and sufficient conditions for the curves with timelike(1,3)-normal plane to be (1,3)-Bertrand curves and we give the related examples forthese curves.

Keywords

• Bertrand curve
• Minkowski space-time
• Frenet planes.