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Results tagged with riemannian-geometry
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user 5371
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.
12
votes
Nonnegative to Positive Curvature.
Yau asked in 1982 if there is any compact simply connected manifold with nonnegative curvature for which one can prove that it does not admit a metric of positive curvature. This question opens his li …
- 22.3k
16
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Some questions about scalar curvature
A big classification result that I'm aware of is due to Gromov and Lawson.
Theorem. Let $M$ be a compact simply connected manifold of dimension $\geq 5$, which is not a spin. Then $M$ admits a met …
- 22.3k