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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.
16
votes
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
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