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Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.

8 votes
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907 views

If a (distance) metric on a connected Riemannian manifold locally agrees with the Riemannian...

Let $(M,g)$ be a connected Riemannian manifold. Let $d_g$ be the induced distance metric of $g$. Now let $d$ be some other metric on $M$. Suppose that for each $x \in M$, there is a neighborhood $U$ …
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