Ruled surfaces right normalized

This paper deals with skew ruled surfaces \(\varPhi\) in the Euclidean space \(\mathbb{E}^{3}\) which are right normalized, that is they are equipped with relative normalizations, whose support function is of the form \(q(u,v) = \frac{f(u) + g(u)\, v}{w(u,v)}\), where \(w^2(u,v)\) is the discriminan...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2017-06
Main Authors: Stamatakis, Stylianos, Papadopoulou, Ioanna-Iris
Format: Article
Language:English
Subjects:
Euclidean geometry
Euclidean space
Fields (mathematics)
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper deals with skew ruled surfaces \(\varPhi\) in the Euclidean space \(\mathbb{E}^{3}\) which are right normalized, that is they are equipped with relative normalizations, whose support function is of the form \(q(u,v) = \frac{f(u) + g(u)\, v}{w(u,v)}\), where \(w^2(u,v)\) is the discriminant of the first fundamental form of \(\varPhi\). This class of relatively normalized ruled surfaces contains surfaces such that their relative image \(\varPhi^{*}\) is either a curve or it is as well as \(\varPhi\) a ruled surface whose generators are, additionally, parallel to those of \(\varPhi\). Moreover we investigate various properties concerning the Tchebychev vector field and the support vector field of such ruled surfaces.
ISSN:2331-8422