Ellipsoids and elliptic hyperboloids in the Euclidean space ${\Bbb E}^{n+1}$

Dong-Soo Kim

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arXiv · 1302.3920

Ellipsoids and elliptic hyperboloids in the Euclidean space ${\Bbb E}^{n+1}$

Dong-Soo Kim

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Abstract

We establish some characterizations of elliptic hyperboloids (resp., ellipsoids) in the $(n+1)$-dimensional Euclidean space ${\Bbb E}^{n+1}$, using the $n$-dimensional area of the sections cut off by hyperplanes and the $(n+1)$-dimensional volume of regions between parallel hyperplanes. We also give a few characterizations of elliptic paraboloids in the $(n+1)$-dimensional Euclidean space ${\Bbb E}^{n+1}$.

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BibTeX RIS

Dong-Soo Kim. 2013-02-16. Ellipsoids and elliptic hyperboloids in the Euclidean space ${\Bbb E}^{n+1}$. https://arxiv.org/abs/1302.3920

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