Ruled surfaces right normalized

2017/06/21 by Stamatakis, Stylianos, Papadopoulou, Ioanna-Iris
#53A05 #53A15 #53A25 #53A40 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1706.07277

Abstract

This paper deals with skew ruled surfaces \varPhi in the Euclidean space 𝔼³ which are right normalized, that is they are equipped with relative normalizations, whose support function is of the form q(u,v) = (f(u) + g(u) v)/(w(u,v)), where w²(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.

Related

• Notes on relative normalizations of ruled surfaces in the three-dimensional Euclidean space
• On polar relative normalizations of ruled surfaces
• Ruled surfaces asymptotically normalized
• On the Laplace Normal Vector Field of Skew Ruled Surfaces
• Characterizations of Ruled Surfaces in \ℝ³ and of\n Hyperquadrics in \ℝⁿ⁺¹ via Relative Geometric Invariants