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Riemannian Geometry is a subfield of Differential Geometry, which specifically studies "Riemannian Manifolds", manifolds with "Riemannian Metrics", which means that they are equipped with continuous inner products.

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Riemannian manifolds with a unique distance property

Let $M$ be a compact Riemannian manifold with geodesic distance function $d$, of (normalised) diameter $1$. Some of my favourite manifolds $M$ have the property that there exists an integer $k$ such t …
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