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arXiv · 2410.20467

A Local Condition for Totally Skew Embeddings

Zachary Norfolk
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Abstract

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.

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Zachary Norfolk. 2024-10-27. A Local Condition for Totally Skew Embeddings. https://arxiv.org/abs/2410.20467

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