On the integrability of Bertrand curves and Razzaboni surfaces.
type: Item
instance of: scholarly article
title: On the integrability of Bertrand curves and Razzaboni surfaces.
zbMATH Open document ID: 1039.53005
DOI: 10.1016/S0393-0440(02)00130-4
author: W. K. Schief
published in: Journal of Geometry and Physics
publication date: 2003-03-23T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 53A05
Mathematics Subject Classification ID: 53A04
zbMATH DE Number: 1886816
zbMATH Keywords: Razzaboni surfaces
zbMATH Keywords: Bertrand curves
reviewed by: Otto Röschel
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1886816