Geodesic
Characterizations of Euclidean Hyperspheres Under Relatively Normalized Convex Hypersurfaces
Journal for geometry and graphics, Tome 16 (2012) no. 1, pp. 41-46 Cet article a éte moissonné depuis la source Heldermann Verlag

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We treat convex hypersurfaces in the Euclidean space Rn+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 Pick-invariant vanishes identically, then Euclidean hyperspheres are obtained too.
Classification : 53A07
Mots-clés : Convex hypersurfaces, relative normalizations, Pick-invariant, Euclidean hyperspheres 
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     author = {G. Stamou },
     title = {Characterizations of {Euclidean} {Hyperspheres} {Under} {Relatively} {Normalized} {Convex} {Hypersurfaces}},
     journal = {Journal for geometry and graphics},
     pages = {41--46},
     year = {2012},
     volume = {16},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JGG_2012_16_1_JGG_2012_16_1_a4/}
}
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G. Stamou . Characterizations of Euclidean Hyperspheres Under Relatively Normalized Convex Hypersurfaces. Journal for geometry and graphics, Tome 16 (2012) no. 1, pp. 41-46. http://geodesic.mathdoc.fr/item/JGG_2012_16_1_JGG_2012_16_1_a4/