Volume properties and some characterizations of ellipsoids in ${\Bbb E}^{n+1}$

Authors

DONG-SOO KIM
INCHEON KIM
YOUNG HO KIM

DOI

10.3906/mat-2009-36

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

Keywords

Ellipsoid, proper affine hypersphere, volume, cone, strictly convex, homothetic hypersurface, Gauss-Kronecker curvature

First Page

896

Last Page

908

Recommended Citation

KIM, DONG-SOO; KIM, INCHEON; and KIM, YOUNG HO (2021) "Volume properties and some characterizations of ellipsoids in ${\Bbb E}^{n+1}$," Turkish Journal of Mathematics: Vol. 45: No. 2, Article 18. https://doi.org/10.3906/mat-2009-36
Available at: https://journals.tubitak.gov.tr/math/vol45/iss2/18