Ilarslan, KazimNesovic, Emilija2020-06-252020-06-252018closedAccess0219-88781793-6977https://doi.org/10.1142/S0219887818501426https://hdl.handle.net/20.500.12587/7341Nesovic, Emilija/0000-0003-3600-0486In this paper, we define the Bishop frame of a null Cartan curve in Minkowski space-time E-1(4). We obtain the Bishop's frame equations of a null Cartan curve which lies in the timelike hyperplane of E-1(4). We show that a null Cartan cubic lying in the timelike hyperplane of E-1(4) has two Bishop frames, one of which coincides with its Cartan frame. We also derive the Bishop's frame equation of the null Cartan curve which has the third Cartan curvature K-3(s) not equal 0. As an application, we find a solution of the null Betchov-Da Rios vortex filament equation in terms of a null Cartan curve and its Bishop frame, which generates a timelike Hasimoto surface.eninfo:eu-repo/semantics/closedAccessBishop frameCartan framenull Cartan curveMinkowski space-timeArticle15810.1142/S02198878185014262-s2.0-85047139617Q2WOS:000435978200018Q3