VOLUME PROPERTIES AND A CHARACTERIZATION OF ELLIPTIC PARABOLOIDS

VOLUME PROPERTIES AND A CHARACTERIZATION OF ELLIPTIC PARABOLOIDS

We establish a characterization theorem of elliptic paraboloids in the (n+1)-dimensional Euclidean space En+1 with extrinsic properties such as the (n+1)-dimensional volumes of regions enclosed by the hyperplanes and hypersurfaces, and the n-dimensional areas of projections of the sections of hypersurfaces cut off by hyperplanes.