Timeline for A non-Kähler compact complex manifold with negative sectional curvature
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Oct 24, 2023 at 0:46 | answer | added | AmorFati | timeline score: 2 | |
| Apr 22, 2023 at 13:42 | comment | added | Michael Albanese | In particular, if $X$ and $Y$ are unit length and orthogonal, then $K(X, Y) = -\frac{1}{4}[1 + 3g(X, JY)^2]$. The inequality then follows as $0 \leq g(X, JY)^2 \leq 1$. | |
| Sep 28, 2020 at 17:55 | comment | added | Michael Albanese | @GabeK: Thanks. For anyone else who is wondering where the quarter-pinching comes from, it follows from the formula in this answer. | |
| Sep 27, 2020 at 4:28 | comment | added | Gabe K | Any Kahler manifold with constant negative holomorphic sectional curvature (and complex dimension at least 2) has negatively quarter-pinched sectional curvature, so you can obtain compact Kahler examples by taking compact quotients of complex hyperbolic space. | |
| Sep 27, 2020 at 3:11 | history | edited | Michael Albanese | CC BY-SA 4.0 |
deleted 4 characters in body; edited tags; edited title
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| Sep 27, 2020 at 3:09 | comment | added | Michael Albanese | Aside from Riemann surfaces of genus at least two, are you aware of any examples of compact complex manifolds (Kähler or non-Kähler) which admit a metric of negative sectional curvature? | |
| Sep 25, 2020 at 16:48 | history | asked | Samir | CC BY-SA 4.0 |