Timeline for Holomorphic manifolds with an Einstein structure and non constant holomorphic sectional curvature
Current License: CC BY-SA 4.0
11 events
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| Aug 13 at 19:42 | history | became hot network question | |||
| Aug 13 at 12:52 | comment | added | Ali Taghavi | @GabeK Yes I see, thank you | |
| Aug 13 at 12:51 | comment | added | Gabe K | It should definitely be there, but I don’t have a copy on hand to verify. The intuition that a broad class of metrics admit KE metrics is that it should be equivalent to some algebraic condition and I’ve heard experts say that “most” manifolds should satisfy it. However, this is not my area of expertise and there are certainly counterexamples, so I’m not sure how precise this is. | |
| Aug 13 at 12:47 | vote | accept | Ali Taghavi | ||
| Aug 13 at 12:24 | comment | added | Ali Taghavi | @GabeK I guess the reference is Griffith& Harris, yes? | |
| Aug 13 at 12:14 | answer | added | Gabe K | timeline score: 4 | |
| Aug 13 at 12:02 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
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| Aug 13 at 12:02 | comment | added | Gabe K | A very simple example is $\mathbb{CP}^1 \times \mathbb{CP}^1$, but in general one should expect a very broad class (though not all) of Kahler manifolds to admit Einstein metrics. On the other hand, a metric has constant holomorphic sectional curvature only if it is covered by $\mathbb{CP}^n$, $\mathbb{C}^n$ or $\mathbb{CH}^n$ (I.e., the complex space forms). | |
| Aug 13 at 12:01 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
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| Aug 13 at 11:52 | history | edited | Ali Taghavi | CC BY-SA 4.0 |
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| Aug 13 at 11:40 | history | asked | Ali Taghavi | CC BY-SA 4.0 |