
Journal for Geometry and Graphics 16 (2012), No. 1, 041046 Copyright Heldermann Verlag 2012 Characterizations of Euclidean Hyperspheres Under Relatively Normalized Convex Hypersurfaces Georg Stamou Dept. of Mathematics, Aristotle University, 54124 Thessaloniki, Greece stamoug@math.auth.gr We treat convex hypersurfaces in the Euclidean space R^{n+1} which are relatively normalized. The relative normalizations are either independent of geometric magnitudes of the considered convex hypersurface Φ or characterized by the fact that the corresponding support functions depend on elementary symmetric functions of the (Euclidean) principal curvatures of Φ. In the first case two characterizations of Euclidean hyperspheres are given via inequalities. In the second case it is proved that if the Pickinvariant vanishes identically, then Euclidean hyperspheres are obtained too. Keywords: Convex hypersurfaces, relative normalizations, Pickinvariant, Euclidean hyperspheres. MSC: 53A07 [ Fulltextpdf (117 KB)] for subscribers only. 