On polar relative normalizations of ruled surfaces

Authors : IoannaIris Papadopoulou, Stylianos Stamatakis

Pages : 74-79

Doi:10.32323/ujma.395094

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Publication Date : 2018-06-26

Article Type : Research Paper

Abstract :This paper deals with skew ruled surfaces in the Euclidean space $\mathbb{E}^{3}$ which are equipped with polar normalizations, that is, relative normalizations such that the relative normal at each point of the ruled surface lies on the corresponding polar plane. We determine the invariants of a such normalized ruled surface and we study some properties of the Tchebychev vector field and the support vector field of a polar normalization. Furthermore, we study a special polar normalization, the relative image of which degenerates into a curve.
Keywords : Pick invariant, Polar normalizations, Ruled surfaces, Tchebychev vector field