Answer by Pietro Majer for Is Riemannian distance function equivalent to...
This equivalence between distances (even on metric space more in general) is exactly the uniform equivalence: the distance $d$ and $d'$ (in your case the Euclidean distance) induce the same uniform...
View ArticleIs Riemannian distance function equivalent to Euclidean one?
Consider the Riemannian manifold $\mathbb{R}^n$ and a smooth Riemannian metric $G:\mathbb{R}^n\rightarrow\mathbb{R}^{n\times{n}}$. We know that if $w_1I_n\leq{G}(x)\leq{w_2}I_n$ for some...
View Article
More Pages to Explore .....
