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This paper deals with relative normalizations of skew ruled surfaces in theEuclidean space $\mathbb{E}^{3}$. In section 2 we investigate some new formulaeconcerning the Pick invariant, the relative curvature, the relative meancurvature and the curvature of the relative metric of a relatively normalizedruled surface $\varPhi$ and in section 3 we introduce some specialnormalizations of it. All ruled surfaces and their corresponding normalizationsthat make $\varPhi$ an improper or a proper relative sphere are determined insection 4. In the last section we study ruled surfaces, which are\emph{centrally} normalized, i.e., their relative normals at each point lie onthe corresponding central plane. Especially we study various properties of theTchebychev vector field. We conclude the paper by the study of the centralimage of $\varPhi$.

Notes on relative normalizations of ruled surfaces in the three-dimensional Euclidean space