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Results tagged with manifolds
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user 119418
A manifold is a topological space that locally resembles Euclidean space near each point. More precisely, each point of an n-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension n.
13
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1
answer
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Are there examples of Einstein manifolds with unbounded curvature?
Are there any known examples of Einstein manifolds $(M, g)$ such that $$\sup_{x \in M} \|\text{Rm}(x) \| = \infty$$
I'm looking for these examples because they might provide a counter-example to a problem …
- 659
4
votes
0
answers
188
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Classifying singularities of the Ricci flow
Indeed, since there are examples of Einstein manifolds with unbounded curvature, it seems the authors made a mistake. … And actually I can't find any other source where Einstein manifolds with negative scalar curvature are classified as a Type III singularity. …
- 659
3
votes
0
answers
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Geometric intuition behind definition of $\delta$-necklike points of the Ricci flow
In "The Ricci Flow: An Introduction", the authors define a $\delta$-necklike point of the Ricci flow as a point $(x, t)$ where $$\|\text{Rm} - R (\theta \otimes \theta)\| \leq \delta \|\text{Rm}\|$$
f …
- 659