  We consider hypersurfaces in the real Euclidean space $\mathbb{R}^{n+1}$
($n\geq2$) which are relatively normalized. We give necessary and sufficient
conditions a) for a surface of negative Gaussian curvature in $\mathbb{R}^3$ to
be ruled, b) for a hypersurface of positive Gaussian curvature in
$\mathbb{R}^{n+1}$ to be a hyperquadric and c) for a relative normalization to
be constantly proportional to the equiaffine normalization.
