Questions tagged [ricci-curvature]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
1
vote
1answer
113 views

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)...
2
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}(...
3
votes
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 ...