Metrisability of projective surfaces and pseudo-holomorphic curves
- We show that the metrisability of an oriented projective surface is equivalent to the existence of pseudo-holomorphic curves. A projective structure p and a volume form σ on an oriented surface M equip the total space of a certain disk bundle Z→M with a pair (Jp,Jp,σ) of almost complex structures. A conformal structure on M corresponds to a section of Z→M and p is metrisable by the metric g if and only if [g]:M→Z is a pseudo-holomorphic curve with respect to Jp and Jp,dAg.
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| Author: | Thomas MettlerORCiDGND |
|---|---|
| URN: | urn:nbn:de:hebis:30:3-692316 |
| DOI: | https://doi.org/10.1007/s00209-020-02586-6 |
| ISSN: | 1432-1823 |
| Parent Title (English): | Mathematische Zeitschrift |
| Publisher: | Springer |
| Place of publication: | Berlin ; Heidelberg |
| Document Type: | Article |
| Language: | English |
| Date of Publication (online): | 2020/08/08 |
| Date of first Publication: | 2020/08/08 |
| Publishing Institution: | Universitätsbibliothek Johann Christian Senckenberg |
| Release Date: | 2022/10/20 |
| Volume: | 298 |
| Issue: | 1-2 |
| Page Number: | 10 |
| First Page: | 69 |
| Last Page: | 78 |
| Note: | Open Access funding provided by Projekt DEAL. |
| Note: | A part of the research for this article was carried out while the author was visiting FIM at ETH Zürich. The author would like to thank FIM for its hospitality and DFG for partial support via the priority programme SPP 2026 “Geometry at Infinity”. |
| Note: | Institut: Informatik und Mathematik |
| HeBIS-PPN: | 502143320 |
| Institutes: | Informatik und Mathematik / Mathematik |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Sammlungen: | Universitätspublikationen |
| Licence (German): |  Creative Commons - Namensnennung 4.0 |
