Generalized Bertrand Curves with Spacelike $\left(1,3\right) $-Normal Plane in Minkowski Space-Time

Authors: ALİ UÇUM, OSMAN KEÇİLİOĞLU, KAZIM İLARSLAN

Abstract: In this paper, we reconsider the $(1,3)$-Bertrand curves with respect to the casual characters of a $\left( 1,3\right) $-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 $\left( 1,3\right) $-normal plane in Minkowski space-time. We obtain the necessary and sufficient conditions for the curves with spacelike $\left( 1,3\right) $-normal plane to be $(1,3)$-Bertrand curves and we give the related examples for these curves.

Keywords: Bertrand curve, Minkowski space-time, Frenet planes

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