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

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If a triangle can be displaced without distortion, must the surface have constant curvature?

The integral over a triangle of the curvature is equal to the difference between the sum of angles for a triangle in a flat surface (that is, $\pi$) and the actual sum of angles for that triangle. $\s …
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