Turkish Journal of Mathematics
Abstract
Suppose that $M$ is a strictly convex and closed hypersurface in ${\Bbb E}^{n+1}$ with the origin $o$ in its interior. We consider the homogeneous function $g$ of positive degree $d$ satisfying $M=g^{-1}(1)$. Then, for a positive number $h$ the level hypersurface $g^{-1}(h)$ of $g$ is a homothetic hypersurface of $M$ with respect to the origin $o$. In this paper, for tangent hyperplanes $\Phi_h$ to $g^{-1}(h)$ ($0
DOI
10.3906/mat-2009-36
Keywords
Ellipsoid, proper affine hypersphere, volume, cone, strictly convex, homothetic hypersurface, Gauss-Kronecker curvature
First Page
896
Last Page
908
Recommended Citation
KIM, D, KIM, I, & KIM, Y. H (2021). Volume properties and some characterizations of ellipsoids in ${\Bbb E}^{n+1}$. Turkish Journal of Mathematics 45 (2): 896-908. https://doi.org/10.3906/mat-2009-36
