2005/06/09 by Gordana Stojanovic, Stojanovic, Gordana
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG
paper · pdf · doi:10.48550/arxiv.math/0506173
arxiv created 2005/06/09 · arxiv updated 2009/12/01
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.