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  • Küçük Resim
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    Characterizations of timelike slant helices in Minkowski 3-space
    (Univ Osijek, Dept Mathematics, 2014) Gok, Ismail; Nurkan, Semra Kaya; Ilarslan, Kazim; Kula, Levent; Altinok, Mesut
    In this paper, we investigate the tangent indicatrix, the principal normal indicatrix and the binormal indicatrix of a timelike curve in Minkowski 3-space E-1(3) and we construct their Frenet equations and curvature functions. Moreover, we obtain some differential equations which characterize a timelike curve to be a slant helix by using the Frenet apparatus of a spherical indicatrix of the curve. Also, related examples and their illustrations are given.
  • Küçük Resim
    Öğe
    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.