Embeddings With Multiple Regularity

Details Embeddings With Multiple Regularity Embeddings With Multiple Regularity

2005-06-09

arxiv.org/abs/math/0506173v1

Mathematics

Differential Geometry

Scientific paper

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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