Timeline for Is Thierry Aubin’s theorem true on Hermitian manifolds?
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
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| Sep 28, 2017 at 16:02 | vote | accept | C.F.G | ||
| S Sep 18, 2017 at 6:40 | history | suggested | C.F.G | CC BY-SA 3.0 |
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| Sep 18, 2017 at 5:20 | review | Suggested edits | |||
| S Sep 18, 2017 at 6:40 | |||||
| Sep 10, 2017 at 21:55 | history | edited | L.F. Cavenaghi | CC BY-SA 3.0 |
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| Sep 10, 2017 at 19:00 | comment | added | Deane Yang | I think the point of the question is asking what is known assuming only Hermitian and not necessarily Kahler. | |
| Sep 10, 2017 at 18:05 | history | edited | L.F. Cavenaghi | CC BY-SA 3.0 |
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| Sep 10, 2017 at 17:56 | comment | added | L.F. Cavenaghi | @SebastianGoette, please, consider to see my edit, in fact I was mistaken. | |
| Sep 10, 2017 at 17:56 | history | edited | L.F. Cavenaghi | CC BY-SA 3.0 |
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| Sep 10, 2017 at 17:47 | comment | added | L.F. Cavenaghi | @SebastianGoette, perhaps I am mixing things, but at Joyce's book (Compact manifolds with special holonomy) he proposes a general statement for Calabi-Yau theorem similar to my last comment. From such statement we can yield similar results as: if $c_1(M) = 0$ then there exists a K\"ahler-Ricci flat metric on $M$. | |
| Sep 10, 2017 at 17:38 | comment | added | L.F. Cavenaghi | @SebastianGoette, If I am not mistaken, provided $c_1(M) > 0$, $M$ is compact and Kaehler, we have a $(1,1)$-form $\rho'$ at the same cohomology class of the Ricci form $\rho$ of the initial K\"ahler metric on $M$. By Calabi-Yau theorem we can find a K\"ahler metric such the Ricci form is $\rho'$. | |
| Sep 10, 2017 at 16:54 | comment | added | Sebastian Goette | Which Calabi-Yau theorem are you referring to? If I remember correctly, there are additional conditions needed if $c_1(M)>0$, see wikipedia. | |
| Sep 10, 2017 at 2:38 | history | edited | L.F. Cavenaghi | CC BY-SA 3.0 |
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| Sep 10, 2017 at 2:37 | comment | added | L.F. Cavenaghi | If I am not mistaken just in the Kahler case, sorry for not pointing it out. | |
| Sep 10, 2017 at 2:19 | comment | added | Fan Zheng | So does the condition "Ricci is nonnegative everywhere and positive at a point" imply the first Chern class is positive? | |
| Sep 9, 2017 at 23:55 | history | answered | L.F. Cavenaghi | CC BY-SA 3.0 |