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 ...
4 votes

Ricci flow on Kähler manifold

Read all about it in J. Song's notes from 2012.
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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 ...
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 ...
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4 votes
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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
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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}...
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