A characterization of the ellipsoid in terms of pairs of sections associated by a harmonic homology
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917463288971264 |
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| author | Morales-Amaya, Efrén |
| author_facet | Morales-Amaya, Efrén |
| contents | Let $K$ be a convex body in an affine chart of the $n$ dimensional real Projective space $\mathbb{RP}^n$, $n \geq 3$, let $H$ be a hyperplane which is not a support hyperplane of $K$ and let $p_1,p_2 \in \mathbb{RP}^n \setminus H$ be two distinct interior points of $K$. In this work we prove that if for every $(n-2)$-plane $l \subset H$, there exists a harmonic homology, with plane $G$ and center $τ$, such that $l\subset G$, $τ\in H$ and which maps the hypersection of $K$ defined by aff$\{p_1, l\}$ onto the hypersection of $K$ defined by aff$\{p_2, l\}$, then $K$ is an ellipsoid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_04398 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A characterization of the ellipsoid in terms of pairs of sections associated by a harmonic homology Morales-Amaya, Efrén Metric Geometry Let $K$ be a convex body in an affine chart of the $n$ dimensional real Projective space $\mathbb{RP}^n$, $n \geq 3$, let $H$ be a hyperplane which is not a support hyperplane of $K$ and let $p_1,p_2 \in \mathbb{RP}^n \setminus H$ be two distinct interior points of $K$. In this work we prove that if for every $(n-2)$-plane $l \subset H$, there exists a harmonic homology, with plane $G$ and center $τ$, such that $l\subset G$, $τ\in H$ and which maps the hypersection of $K$ defined by aff$\{p_1, l\}$ onto the hypersection of $K$ defined by aff$\{p_2, l\}$, then $K$ is an ellipsoid. |
| title | A characterization of the ellipsoid in terms of pairs of sections associated by a harmonic homology |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2605.04398 |