Characterizations of Ruled Surfaces in ${\mathbb{R}}^3$ and of Hyperquadrics in ${\mathbb{R}}^{n+1}$ via Relative Geometric Invariants

Stylianos Stamatakis, Ioannis Kaffas, Ioanna-Iris Papadopoulou

We consider hypersurfaces in the real Euclidean space ${\mathbb{R}}^{n+1}$ ($n\ge 2$) which are relatively normalized. We give necessary and sufficient conditions a) for a surface of…