Timeline for Does every non-compact hyperbolic manifold admit compact complex submanifolds?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Mar 2, 2022 at 20:39 | comment | added | Mohan Ramachandran | Any simply connected complete Kahler manifold with negative sectional curvature has negative holomorphic sectional curvature ,and is a Stein manifold . Any complex submanifold of it has negative holomorphic sectional curvature . | |
| Feb 26, 2022 at 13:19 | history | edited | YCor | CC BY-SA 4.0 |
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| Feb 26, 2022 at 12:59 | comment | added | LeechLattice | Does the title imply that $X$ should be non-compact? | |
| Feb 26, 2022 at 1:20 | comment | added | Jason Starr | More counterexamples arise from the complex hyperbolic spaces: maths.dur.ac.uk/users/j.r.parker/img/NCHG.pdf | |
| Feb 25, 2022 at 23:37 | comment | added | Jason Starr | What about the open unit disk with its hyperbolic metric? | |
| Feb 25, 2022 at 20:14 | comment | added | Igor Belegradek | I don't know much about complex submanifolds but e.g. suppose $X$ is a complex hyperbolic manifold with infinite cyclic fundamental group. Thus the universal cover of $X$ is the complex hyperbolic space. Does $X$ contain a compact complex submanifold (of positive dimension)? | |
| Feb 25, 2022 at 19:43 | history | asked | AmorFati | CC BY-SA 4.0 |