Ruled surfaces right normalized

This paper deals with skew ruled surfaces $\Phi$ 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 $\Phi$. This class of relatively normalized ruled surfaces contains surfaces such that their relative image ${\Phi }^{\ast }$ is either a curve or it is as well as $\Phi$ a ruled surface whose generators are, additionally, parallel to those of $\Phi$. Moreover we investigate various properties concerning the Tchebychev vector field and the support vector field of such ruled surfaces.