Eine Übertragung des Satzes von Bonnet auf Regelflächen im einfach isotropen Raum. (A transfer of Bonnet's theorem to ruled surfaces in the simply isotropic space) (Q1107838)

This paper contains a transfer of Bonnet's theorem onto ruled surfaces in the isotropic space \(J_ 3^{(1)}\). Bonnet's classical theorem about ruled surfaces in the three-dimensional Euclidean space does not hold in \(J_ 3^{(1)}\). To get to an isotropic version of this theorem the terms ``geodesic line'' and ``isogonal-trajectory of the generators'' are replaced by new adapted properties of curves on ruled surfaces which are adapted to the isotropic space.