Timeline for Real diffeomeorphism preserving the space of Holomorphic vector fields
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 20, 2019 at 20:32 | comment | added | Ali Taghavi | @DanielAsimov Thank you very much for your attention to my question and your helpfull comment. | |
| Oct 20, 2019 at 5:59 | comment | added | Daniel Asimov | Hurwitz's theorem states that for a Riemann surface of genus 2 or more, the size of its full automorphism group is no greater than 84(g-1). Any non-trivial holomorphic flow consists of infinitely many automorphisms, so cannot exist on a higher genus Riemann surface. | |
| Sep 11, 2017 at 5:57 | vote | accept | Ali Taghavi | ||
| Sep 10, 2017 at 16:29 | review | Close votes | |||
| Sep 10, 2017 at 19:55 | |||||
| Sep 10, 2017 at 16:03 | answer | added | Ben McKay | timeline score: 2 | |
| Sep 10, 2017 at 7:39 | comment | added | Ali Taghavi | @BenMcKay Is there a complex manifold for which $G$ is small for example the G action is not transitive? | |
| Sep 10, 2017 at 6:54 | comment | added | Ali Taghavi | Or $M$ is an open set in the complex plane? For $M=\mathbb{C}$ is there a diffeomorphism different from $az+b$ or $a\bar{z}+b$? | |
| Sep 10, 2017 at 6:46 | comment | added | Ali Taghavi | @BenMcKay Thnks for your comment. Yes I mean global vector fields.What is a reference for the fact you mentioned for genus 2? Moreover what is the structure of $G$ when $M=\mathbb{C}$? | |
| Sep 10, 2017 at 6:29 | comment | added | Ben McKay | Do you mean globally defined holomorphic vector fields? Many complex manifolds only have one globally defined holomorphic vector field: 0. For example, any compact Riemann surface of genus 2 or more. In that case, your group $G$ is the group of all diffeomorphisms, not a Lie group. | |
| Sep 9, 2017 at 19:48 | history | asked | Ali Taghavi | CC BY-SA 3.0 |