Timeline for Obstructions for a foliation to be transformed to a Frenet foliation
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 31, 2018 at 15:56 | comment | added | André Henriques | Yes, locally this is possible: both a real analytic curves, and any real analytic diffeomorphism between these curves extends to a holomorphic diffeomorphism between neighbourhoods of these curves. That's called analytic continuation. | |
| Jan 31, 2018 at 15:53 | comment | added | Ali Taghavi | I mean locally (not necessarily global bioholomorphism). | |
| Jan 31, 2018 at 15:51 | comment | added | André Henriques | The only biholomorphic maps $\mathbb C\to\mathbb C$ are of the form $z\mapsto az+b$, but there exist many diffeomorphisms $\mathbb R^2\to \mathbb R^2$. | |
| Jan 31, 2018 at 9:57 | comment | added | Ali Taghavi | Thanks for your answer. Can a bioholomorphic maps in the plane carry $y=x^2$ to $y=x^3$? I mean that: is not the Riemann mapping theorem an obstruction for your statement? | |
| Jan 31, 2018 at 9:19 | history | answered | André Henriques | CC BY-SA 3.0 |