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arXiv · 1208.5361

Some characterizations of spheres and elliptic paraboloids II

Dong-Soo Kim·Young Ho Kim
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Abstract

We show some characterizations of hyperspheres in the $(n+1)$-dimensional Euclidean space ${\Bbb E}^{n+1}$ with intrinsic and extrinsic properties such as the $n$-dimensional area of the sections cut off by hyperplanes, the $(n+1)$-dimensional volume of regions between parallel hyperplanes, and the $n$-dimensional surface area of regions between parallel hyperplanes. We also establish two characterizations of elliptic paraboloids in the $(n+1)$-dimensional Euclidean space ${\Bbb E}^{n+1}$ with the $n$-dimensional area of the sections cut off by hyperplanes and the $(n+1)$-dimensional volume of regions between parallel hyperplanes. For further study, we suggest a few open problems.

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Dong-Soo Kim, Young Ho Kim. 2012-08-27. Some characterizations of spheres and elliptic paraboloids II. https://arxiv.org/abs/1208.5361

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