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 casual characters of (1,3)-normal plane which is a plane spanned by the principal normal and the second binormal vector fields of the given curve. Here, we restrict our investigation of (1,3)-Bertrand curves to the timelike (1,3)-normal plane in Minkowski space-time. 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 for these curves.