A relative-geometric treatment of ruled surfaces

We consider relative normalizations of ruled surfaces with non-vanishing Gaussian curvature K in the Euclidean space , which are characterized by the support functions ( α ) q  = | K | α for . All ruled surfaces for which the relative normals, the Pick invariant or the Tchebychev vector field have s...

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Bibliographic Details
Published in:Beiträge zur Algebra und Geometrie 2012-10, Vol.53 (2), p.297-309
Main Authors: Stamou, Georg, Stamatakis, Stylianos, Delivos, Ioannis
Format: Article
Language:English
Subjects:
Algebra
Algebraic Geometry
Convex and Discrete Geometry
Geometry
Mathematics
Mathematics and Statistics
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Summary:We consider relative normalizations of ruled surfaces with non-vanishing Gaussian curvature K in the Euclidean space , which are characterized by the support functions ( α ) q  = | K | α for . All ruled surfaces for which the relative normals, the Pick invariant or the Tchebychev vector field have some specific properties are determined. We conclude the paper by the study of the affine normal image of a non-conoidal ruled surface.
ISSN:0138-4821
2191-0383
DOI:10.1007/s13366-011-0035-9