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


  • ALİ UCUM Department of Mathematics, Faculty of Arts and Sciences, Kırıkkale University, 71450 Yahsihan, Kırıkkale, TURKEY
  • OSMAN KEÇİLİOĞLU Department of Statistics, Faculty of Sciences and Arts, Kırıkkale University, 71450 Yahsihan, Kırıkkale, TURKEY
  • KAZIM İLARSLAN Department of Mathematics, Faculty of Arts and Sciences, Kırıkkale University, 71450 Yahsihan, Kırıkkale, TURKEY


Bertrand curve, Minkowski space-time, Frenet planes.


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.


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