Regular Maps on Euclidean Spaces and Tori

Abstract

A map from a manifold to a Euclidean space is said to be k-regular if the image of any distinct k points are linearly independent. In this paper, we give some lower bounds of the dimension of the ambient Euclidean space for complex k-regular maps on Euclidean spaces.

This paper has been withdrawn by the author because the content of this paper has been corrected and merged with another paper arXiv:1511.01601