Timeline for A question on anti-self-dual Weyl curvature of Kaehler surfaces
Current License: CC BY-SA 3.0
5 events
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| Dec 30, 2015 at 14:09 | comment | added | Robert Bryant | It is certainly not true in general. The space of isometry classes of Kähler-Einstein metrics on complex surfaces that are Fano (i.e., have positive Einstein constant) and have the property that $W_-$ has a double eigenvalue at every point is only three dimensional, and this is not large enough to account for all the Fano surfaces, or even the nonsingular cubic surfaces in $\mathbb{P}^3$. | |
| Dec 29, 2015 at 7:35 | vote | accept | littlelittlelittle | ||
| Dec 29, 2015 at 7:15 | comment | added | littlelittlelittle | Thank you very much for your answer. If we further restrict to Fano Kaehler-Einstein metric, may it be true? (They have been classified by Gang Tian, but I couldn't find any paper describing $W^-$ of these manifolds) | |
| Dec 28, 2015 at 12:45 | history | edited | Robert Bryant | CC BY-SA 3.0 |
Added some clarifying remarks
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| Dec 28, 2015 at 9:17 | history | answered | Robert Bryant | CC BY-SA 3.0 |