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Results tagged with riemannian-geometry
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user 48208
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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Must a manifold covered by $ S^n $ admit a metric of constant positive sectional curvature?
Suppose that the smooth manifold $ M $ has the n-sphere for its universal cover (in the topological sense). Does there exist a Riemannian metric on $ M $ (not necessarily compatible with the covering …
- 19.3k
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Riemannian metric on the sphere with at least one negative sectional curvature at every point
Does there exist a Riemannian metric on the $n$-sphere ($n > 2$) such that at each point some (but not every) sectional curvature is negative?
For $n=2$ it is easily seen that such a metric cannot e …
- 5,891