Generalized Bertrand Curves with Spacelike (1,3)(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 a (1, 3) -normal plane that 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 spacelike (1, 3) -normal plane in Minkowski space-time. We obtain the necessary and sufficient conditions for the curves with spacelike (1, 3) -normal plane to be (1, 3) -Bertrand curves and we give the related examples for these curves.