Simplices with fixed volumes of codimension 2 faces in a continuous deformation
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915111150551040 |
|---|---|
| author | Zhang, Lizhao |
| author_facet | Zhang, Lizhao |
| contents | For any $n$-dimensional simplex in the Euclidean space $\mathbb{R}^n$ with $n\ge 4$, it is asked that if a continuous deformation preserves the volumes of all the codimension 2 faces, then is it necessarily a \emph{rigid} motion. While the question remains open and the general belief is that the answer is affirmative, for all $n\ge 4$, we provide counterexamples to a variant of the question where $\mathbb{R}^n$ is replaced by a pseudo-Euclidean space $\mathbb{R}^{p,n-p}$ for some unspecified $p\ge 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_15817 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Simplices with fixed volumes of codimension 2 faces in a continuous deformation Zhang, Lizhao Metric Geometry Combinatorics 52C25 (Primary), 52B11, 51M25 (Secondary) For any $n$-dimensional simplex in the Euclidean space $\mathbb{R}^n$ with $n\ge 4$, it is asked that if a continuous deformation preserves the volumes of all the codimension 2 faces, then is it necessarily a \emph{rigid} motion. While the question remains open and the general belief is that the answer is affirmative, for all $n\ge 4$, we provide counterexamples to a variant of the question where $\mathbb{R}^n$ is replaced by a pseudo-Euclidean space $\mathbb{R}^{p,n-p}$ for some unspecified $p\ge 2$. |
| title | Simplices with fixed volumes of codimension 2 faces in a continuous deformation |
| topic | Metric Geometry Combinatorics 52C25 (Primary), 52B11, 51M25 (Secondary) |
| url | https://arxiv.org/abs/2307.15817 |