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Results tagged with riemannian-geometry
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user 142456
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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Is the injectivity radius (semi) continuous on a non-complete Riemannian manifold?
I believe the following proof shows that it is lower semi-continuous, but I do not know a whether it's continuous (or a counterexample), and like OP, would be interested.
The idea is to take a ball …
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