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Results tagged with riemannian-geometry
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user 7311
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.
20
votes
Accepted
Riemannian metric induced by a metric
Here is a closely related question that may have been what the OP was driving at. Suppose that you ONLY know a Riemannian manifold as a metric space---that is you know the point set and the distance b …
- 15.3k
6
votes
Action of the group of isometries on a manifold
It is easy to see that any metrically homogeneous, locally compact, metric space, $X$, is complete. If $p$ is some point of $X$ then, by local compactness, for some $\epsilon > 0$, the closed $\epsilo …
- 15.3k
7
votes
Global description of the Levi-Civita connection
See my response (number 4) to the MO question:
Exponential map and covariant derivative
There is a Math Review article by Kuranishi there of the paper "Sprays" by Ambrose, Singer, and Palais (in whi …
- 15.3k