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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.
8
votes
Do cotangent bundles have "bounded geometry"?
Let me complement (and compliment?) Igor's answer by providing an explicit definition of bounded geometry from the work of Cheeger and Gromov.
A Riemannian manifold $(M,g)$ has $C^k$-bounded geometr …
6
votes
Voronoi cells and the dual complexes in Riemannian manifolds
At least partial answers to your first two questions can be found in the brief article called Delaunay triangulations and Voronoi diagrams for Riemannian manifolds by Leibon and Letscher available her …