Timeline for Deform a non-Kähler manifold to a Kähler one
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Jul 25, 2021 at 2:40 | comment | added | AmorFati | A deformation preserves Betti numbers (since all fibres will be diffeomorphic, in particular, homeomorphic). Kähler implies that the odd Betti numbers must be even, so you'll need to restrict your consideration to non-Kähler manifolds whose odd Betti numbers are even. | |
| Jul 24, 2021 at 23:46 | comment | added | Tom | @Very Confused, I mean (1), without Kähler structure, so $\mathbb P^1$ is always Kähler no matter which metric it choose. | |
| Jul 24, 2021 at 21:53 | comment | added | AmorFati | By non-Kähler manifold, do you mean (1) a complex manifold which carries no Kähler structure, or (2) a complex manifold with a structure that happens to be non-Kähler? For example, if we consider $\mathbb{P}^1$ equipped with a Hermitian non-Kähler metric, this gives an example of (2), but not (1). Hopf surfaces give examples of (1) but not (2). | |
| Jun 29, 2021 at 12:37 | history | edited | Tom | CC BY-SA 4.0 |
edited title
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| Jun 28, 2021 at 17:09 | history | asked | Tom | CC BY-SA 4.0 |