Timeline for Different complexifications of a real analytic Riemannian manifold
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Mar 28, 2016 at 9:33 | comment | added | Ben McKay | Biholomorphisms of a complex $n$-dimensional manifold depend on $2n$ functions of $n$ variables, while our function $f$ is one essentially arbitrary function of $2n$ variables, so it seems unlikely that a biholomorphism can identify such metrics. Of course, this isn't a rigorous argument. But $f$ can have compact support here, so it is easy to make a rigorous argument. | |
| Mar 28, 2016 at 9:24 | comment | added | Sebastian Goette | Is it clear that the new metric is not biholomorphic to the old one? | |
| Mar 27, 2016 at 20:44 | history | edited | Ben McKay | CC BY-SA 3.0 |
better answer
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| Mar 27, 2016 at 20:26 | history | answered | Ben McKay | CC BY-SA 3.0 |