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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). (German) Zbl 0653.53009

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.
Reviewer: R.Arnold

MSC:

53A25 Differential line geometry
53A40 Other special differential geometries
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References:

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