Geodesic
Characterizations of Ruled Surfaces in R3 and of Hyperquadrics in Rn+1 via Relative Geometric Invariants
Journal for geometry and graphics, Tome 18 (2014) no. 2, pp. 217-223.

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We consider hypersurfaces in the real Euclidean space Rn+1 (n ≥ 2) which are relatively normalized. We give necessary and sufficient conditions (a) for a surface of negative Gaussian curvature in R3 to be ruled, (b) for a hypersurface of positive Gaussian curvature in Rn+1 to be a hyperquadric and (c) for a relative normalization to be constantly proportional to the equiaffine normalization.
Classification : 53A05, 53A07, 53A15, 53A25, 53A40
Mots-clés : Ruled surfaces, ovaloids, hyperquadrics, equiaffine normalization, Pick-invariant 
@article{JGG_2014_18_2_JGG_2014_18_2_a6,
     author = {S. Stamatakis and I. Kaffas and I.-I. Papadopoulou },
     title = {Characterizations of {Ruled} {Surfaces} in {R\protect\textsuperscript{3}} and of {Hyperquadrics} in {R\protect\textsuperscript{n+1}} via {Relative} {Geometric} {Invariants}},
     journal = {Journal for geometry and graphics},
     pages = {217--223},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2014},
     url = {http://geodesic.mathdoc.fr/item/JGG_2014_18_2_JGG_2014_18_2_a6/}
}
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S. Stamatakis; I. Kaffas; I.-I. Papadopoulou . Characterizations of Ruled Surfaces in R3 and of Hyperquadrics in Rn+1 via Relative Geometric Invariants. Journal for geometry and graphics, Tome 18 (2014) no. 2, pp. 217-223. http://geodesic.mathdoc.fr/item/JGG_2014_18_2_JGG_2014_18_2_a6/