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Admissible Mannheim curves in pseudo-Galilean space \(G_3^1\). (English) Zbl 1241.53008

Summary: In this paper, admissible Mannheim partner curves are defined in pseudo-Galilean space \(G_3^1\). Moreover, it is proved that the distance between the reciprocal points of admissible Mannheim curves and the torsions of these curves are constant. Furthermore, the relations for curvatures and torsions of these curves and Schell Theorem are obtained. Finally, a result about these curves being general helix is given.

MSC:

53A35 Non-Euclidean differential geometry
51M30 Line geometries and their generalizations