Timeline for Analytic representatives for Kahler classes
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Jul 25, 2017 at 8:30 | comment | added | Robert Bryant | @HassanJolany: I don't understand your objection. By hypothesis, the class $[\omega]$ has a Kähler representative (i.e., a positive closed $(1,1)$-form), namely $\omega$ itself; that's what it means for it to be a Kähler class, rather than just a $(1,1)$-class. | |
| Jul 25, 2017 at 3:18 | comment | added | user21574 | @RobertBryant No, your answer need to be revised! You may never have such initial metric when $0<kod(X)<\dim X$. See hal.archives-ouvertes.fr/hal-01413754 | |
| Jul 2, 2014 at 19:06 | comment | added | Robert Bryant | It's in the literature, but I don't remember an explicit reference. It follows immediately, though, from Bando's original 1987 result that any solution of Ricci-flow on a compact Riemannian manifold is, at any positive time, real-analytic in geodesic normal coordinates coupled with the fact that, in the Kähler-Ricci case, the complex structure $J$ is parallel with respect to each metric $g(t)$ associated to $\omega(t)$ for $t>0$. This implies that $J$ is real-analytic in geodesic normal coordinates for each $g(t)$ and hence $J$-holomorphic functions are real-analytic in such coordinates. | |
| Jul 2, 2014 at 18:39 | vote | accept | Italo | ||
| Jul 2, 2014 at 18:39 | comment | added | Italo | Many thanks! can you tell me a reference where it is proved that the evolution of a smooth Kahler metric through Kahler Ricci flow is real analytic? | |
| Jul 2, 2014 at 16:32 | history | edited | Robert Bryant | CC BY-SA 3.0 |
Corrected an omission of the linear algebra construction
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| Jul 2, 2014 at 15:05 | history | edited | Robert Bryant | CC BY-SA 3.0 |
Corrected an omission of the linear algebra construction
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| Jul 2, 2014 at 14:55 | comment | added | Robert Bryant | Oh, sorry, I should have remembered that you have to do a linear combination in general. I'll fix that. Thanks for pointing out that oversight. | |
| Jul 2, 2014 at 14:23 | comment | added | Italo | Thank you for the answer. By Kahler Ricci flow you mean $$\partial_{t}\omega_{t}=-Ric(\omega_{t})$$? Sorry but i don't see why $\omega_{0}$ and $\omega_{t}$ are cohomologous. | |
| Jul 2, 2014 at 13:19 | history | answered | Robert Bryant | CC BY-SA 3.0 |