Minkowski versus Euclidean rank for products of metric spaces

Foertsch, T; Schroeder, V (2002). Minkowski versus Euclidean rank for products of metric spaces. Advances in Geometry, 2(2):123-131.

Abstract

We introduce a notion of the Euclidean- and the Minkowski rank for arbitrary metric spaces and we study their behaviour with respect to products. We show that the Minkowski rank is additive with respect to metric products, while additivity of the Euclidean rank only holds under additional assumptions, e.g. for Riemannian manifolds. We also study products with nonstandard product metrics.

We introduce a notion of the Euclidean- and the Minkowski rank for arbitrary metric spaces and we study their behaviour with respect to products. We show that the Minkowski rank is additive with respect to metric products, while additivity of the Euclidean rank only holds under additional assumptions, e.g. for Riemannian manifolds. We also study products with nonstandard product metrics.

Citations

3 citations in Web of Science®
4 citations in Scopus®