13
votes

Accepted

### Ricci flow preserves almost Kahler condition?

The answer is, in general 'no': Under the Ricci-flow, a metric need not remain compatible with $J$ if $J$ is not integrable, even if the associated $2$-form $\omega$ is assumed closed.
I don't see ...

- 101k

4
votes

4
votes

### Curvatures preserved under the Kahler-Ricci flow

I am assuming you are asking the question on a compact Kahler manifold. You can find argument in Mok's paper for the part of non-negativity of holomorphic bisectional curvature (HBSC) is preserved ...

- 506

4
votes

### Reading material for an analytical aspect of Kähler Geometry

Ben Weinkove 5 lectures
The Kähler–Ricci flow on compact Kähler manifolds which has been collected in
Bray, Hubert L. (ed.); Galloway, Greg (ed.); Mazzeo, Rafe (ed.); Sesum, Natasa (ed.), Geometric ...

- 4,085

4
votes

Accepted

### Reading material for an analytical aspect of Kähler Geometry

I'll give an answer that is specifically tailored towards the Kahler-Ricci flow. Hopefully other answers can give some good materials for geometric analysis on Kahler manifolds more generally. For KR ...

- 4,441

2
votes

Accepted

### Schwarz lemma and bisectional curvature lower bound

Their idea is correct, but its formulation (and the chosen notation) is indeed a bit sloppy. What they seem to do, in reality, is to define
$$ - \hat C = \inf _{x \in M} \inf \{ \hat R (e_i, \bar {e_i}...

- 4,810

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