Abstract
We study two classes of surfaces in euclidean 3-space, namelyruled andmolding surfaces, specialsurfaces of revolution (molding surfaces are covered by a plane curve if the plane is rolling over a torse, in particularsurfaces moulures by G.MONGE for a cylindrical torse). The main result: A connected surface hyperosculating molding surfaces in every point is contained in a ruled or in a molding surface; a connected surface hyperosculating in every point surfaces of revolution is a surface of revolution. We characterize hyperosculating molding surfaces by means of the generating torse and study finally molding surfaces having contact of higher order.
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Paukowitsch, H.P. Eine Kennzeichnung der Regel- und Gesimsflächen. J Geom 15, 182–194 (1980). https://doi.org/10.1007/BF01922495
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DOI: https://doi.org/10.1007/BF01922495