TY  - JOUR
A1  - Mettler, Thomas
T1  - Metrisability of projective surfaces and pseudo-holomorphic curves
T2  - Mathematische Zeitschrift
N2  - 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.
Y1  - 2020
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/69231
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-692316
SN  - 1432-1823
N1  - Open Access funding provided by Projekt DEAL.
N1  - 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”.
N1  - Institut: Informatik und Mathematik
VL  - 298
IS  - 1-2
SP  - 69
EP  - 78
PB  - Springer
CY  - Berlin ; Heidelberg
ER  -