Timeline for Can every hyperelliptic genus 3 surface be minimally immersed in flat $T^3$
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 1, 2015 at 19:52 | comment | added | Sebastian | Dear Piojo, I do not understand your comment. Whenever you have a minimal surface with translational periods only, you get two holomorphic spinors, and vice versa. The problem is to find two spinors such that the corresponding real parts of the 2g many $\mathbb C^3$ valued periods span a lattice in euclidean 3-space. | |
| Jul 1, 2015 at 15:40 | comment | added | Piojo | By last line I mean genus 3. | |
| Jul 1, 2015 at 14:48 | comment | added | Piojo | Thanks for your answer Sebastian. I understand that once you have a minimal surface in $T^3$, you get two spinors which define the holomoprhic Gauss map. But I don't think one can always recover the minimal surface from 2 spinors. It is proved in Meeks' paper "The theory of triply periodic minimal surfaces" that hyperelliptic surface of even genus cannot be minimally immersed into $T^3$. But certainly these surfaces admit spinor bundles with enough sections. And in the same paper, Meeks constructed a real 5-dimensional family of minimal embedded genus 2 surfaces in $T^3$. | |
| Jul 1, 2015 at 8:45 | history | edited | Sebastian | CC BY-SA 3.0 |
added 16 characters in body
|
| Jul 1, 2015 at 8:21 | history | answered | Sebastian | CC BY-SA 3.0 |