On the integrability of Bertrand curves and Razzaboni surfaces.
A pair of Bertrand curves is characterized by the property of a common surface of principle normals. Their curvature and torsion are linked by a linear equation with constant coefficients \(\alpha\) and \(\beta.\) A surface \(\Sigma\) is called Razzaboni surface if it is spanned by a one-parameter family of geodesic Bertrand curves with given values of \(\alpha\) and \(\beta.\) There is a surface analogue to the Bertrand pairs of curves: A Razzaboni surface \(\Sigma\) will always determine an associated Razzaboni surface \(\Sigma '\), the locus of the corresponding Bertrand curves. \(\Sigma\) and \(\Sigma '\) are parallel surfaces to each other. Mappings and transformations connected with these surfaces are presented in the paper.
scientific article; zbMATH DE number 1886816
scientific article