Mannheim B-curve couples inminkowski 3-space

Abstract

© 2020 Tamkang University. All rights reserved. In this paper, we define null Cartan Mannheim and pseudo null Mannheim curves in Minkowski 3-space according to their Bishop frames. We obtain the necessary and the sufficient conditions for pseudo null curves to be Mannheim B-curves in terms of their Bishop curvatures. We prove that there are no null Cartan curves in Minkowski 3-space which are Mannheim B-curves, by considering the cases when their Mannheim B-mate curves are spacelike, timelike, null Cartan and pseudo null curves. Finally, we give some examples of pseudo nullMannheim B-curve pairs.