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Generalized Null Bertrand Curves In Minkowski Space-Time
(Univ Al I Cuza, Fac Math, 2014) Aksoyak, Ferdag Kahraman; Gok, Ismail; Ilarslan, Kazim
COKEN and CIFTCI proved that a null Cartan curve in Minkowski space-time E-1(4) is a null Bertrand curve if and only if k(2) is nonzero constant and k(3) is zero. That is, the null curve with non-zero curvature k(3) is not a Bertrand curve in Minkowski space-time E-1(4). So, in this paper we defined a new type of Bertrand curve in Minkowski space-time El for a null curve with non-zero curvature k(3) by using the similar idea of generalized Bertrand curve given by MATSUDA and YOROZU and we called it a null (1, 3)-Bertrand curve. Also, we proved that if a null curve with non-zero curvatures in Minkowski spacetime E-1(4) is a null (1, 3)-Bertrand curve then it is a null helix. We give an example of such curves.