Timelike Mannheim curves in Minkowski 3-space revisited

H. İ. Arıcı, K. İarslan

An important field of study of the theory of curves in Euclidean 3-space is the study of curve pairs with the help of relations between Frenet vectors of two space curves. In searching for pairs of curves such that the tangents, principal normals or binormals of one may be the tangents, principal normals or binormals of the other, there are six cases to be considered. Mannheim curves is one of the curves that emerged as a result of this relationship. Mannheim curves have been studied extensively for different dimensions in both Euclidean spaces and Minkowski spaces. In this paper, we give new results for the timelike Mannheim curves in Minkowski 3-space by using a new approach. According to this approach, the necessary and sufficient conditions including the known results have been obtained for a ptimelike curve to be Mannheim curve in E₁³.

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 16,  supplement issue 3 (2023), pp. 15-27