Some characterizations of Mannheim partner curves in the Minkowski 3-space \(E_{1}^{3}\) (Q2893082)

Whereas a pair of Bertrand curves has common principal normals in corresponding points, for Mannheim partner curves the principal normals of one of the curves coincide with the binormals of the other one in corresponding points. Mannheim partner curves are studied in Minkowski space \(E^3_1\). It is shown that Mannheim's theorem is not valid, that means that a certain cross ratio is not constant. The reviewer could not resolve the following contradiction:NEWLINENEWLINE In Theorem 3.2 it is claimed that for any curve there is another curve so that these curves form a Mannheim pair. But in Theorem 3.4 it is shown that curvature and torsion of a curve belonging to a Mannheim pair obey a linear relation.