Abstract
We introduce (k,l)-regular maps, which generalize two previously studied classes of maps: affinely k-regular maps and totally skew embeddings. We exhibit some explicit examples and obtain bounds on the least dimension of a Euclidean space into which a manifold can be embedded by a (k,l)-regular map. The problem can be regarded as an extension of embedding theory to embeddings with certain non-degeneracy conditions imposed, and is related to approximation theory.
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Stojanovic, G. Embeddings with multiple regularity. Geom Dedicata 123, 1–10 (2006). https://doi.org/10.1007/s10711-006-9055-2
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DOI: https://doi.org/10.1007/s10711-006-9055-2