A Local Condition for Totally Skew Embeddings
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912089387302912 |
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| author | Norfolk, Zachary |
| author_facet | Norfolk, Zachary |
| contents | We introduce a third-order differential condition, analogous to nonzero torsion of a curve, which guarantees a submanifold of Euclidean space is totally skew in a small neighborhood. This condition is used to construct improved totally skew embeddings of $\mathbb{R}^n$, and to solve the totally skew embedding problem for $\mathbb{R}^n$ with $n$ a power of 2. Some algebraic and geometric properties of this condition are also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20467 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Local Condition for Totally Skew Embeddings Norfolk, Zachary Differential Geometry We introduce a third-order differential condition, analogous to nonzero torsion of a curve, which guarantees a submanifold of Euclidean space is totally skew in a small neighborhood. This condition is used to construct improved totally skew embeddings of $\mathbb{R}^n$, and to solve the totally skew embedding problem for $\mathbb{R}^n$ with $n$ a power of 2. Some algebraic and geometric properties of this condition are also discussed. |
| title | A Local Condition for Totally Skew Embeddings |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2410.20467 |