Questions tagged [ricci-curvature]
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7
questions
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1answer
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Is there any Riemannian manifold of zero dimensional isometry group such that
Sorry if this question is belongs to MSE. I have no idea about it.
Question: Is there any Riemannian manifold of zero dimensional isometry group which its Ricci curvature is positive (or maybe zero)...
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votes
0answers
68 views
Joining metrics of positive Ricci curvature
Let $M$ be a smooth manifold such that there is a closed submanifold $S\subset M$ with a Riemannian metric $g_S$ given by the restriction of a Riemannian metric on $M$ satisfying $\mathrm{Ricci}_{g_S}(...
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0answers
128 views
Explicit KE metrics
Does there exist an explicit example of a
Ricci-flat, non-flat metric on a closed manifold?
Kaehler--Einstein, non-flat metric on a closed manifold (excluding metrics on homogeneous spaces and ...
10
votes
2answers
501 views
Deforming metrics from non-negative to positive Ricci curvature
Given a closed Riemannian manifold $(M,g)$ with non-negative Ricci curvature and $dim\geq 3$, when can we deform the metric to a positive Ricci curved one?
I know it's impossible in general due to ...
10
votes
1answer
259 views
Positive Ricci curvature on fiber bundles
My advisor and I are working on Ricci curvature and an anonymous referee pointed out the following conjecture:
Let $F\hookrightarrow M\stackrel{\pi}{\to}B$ be a fiber bundle from a compact manifold ...
4
votes
2answers
149 views
Lower bounds on the Ricci curvature of Kähler submanifolds of $\mathbb{C}^n$
Say that $M$ is a smooth complex algebraic variety inside $\mathbb{C}^n$, and that $M$ has Ricci curvature bounded from below when endowed with the Kähler metric induced by the Euclidean metric of the ...
8
votes
2answers
550 views
Converse to Milnor's theorem on manifolds with nonnegative Ricci curvature
Disclaimer : I suspect the question I am about to ask is really hard, but I just want to know the status of such questions.
Thanks to Milnor, we know that the $\pi_1$ any compact manifold with ...
