On Generalized Timelike Mannheim Curves in Minkowski Space-time

Abstract

In Minkowski space-time, timelike generalized Mannheim curves are studied by Akyigit and et al in [1]. In that paper, the authors take the Mannheim mate alpha* of the timelike curve a as a timelike curve in Minkowski space-time E-1(4). In this statement, the plane spanned by {B-1*, B-2*} becomes a spacelike plane. Thus the other possible cases such as timelike and null for the plane spanned by {B-1*, B-2*} is not considered. In this paper, by taking consideration of all possible causal characters of the plane spanned by{B-1*, B-2*}, we give the necessary and sufficient conditions for timelike curves ME to be generalized timelike Mannheim curves in terms of their curvature functions. Also, the related examples are given.