Pseudoholomorphic curves in S^6 and S^5

  • The octonionic cross product on R7 induces a nearly Kähler structure on S6, the analogue of the Kähler structure of S2 given by the usual (quaternionic) cross product on R3. Pseudoholomorphic curves with respect to this structure are the analogue of meromorphic functions. They are (super-)conformal minimal immersions. We reprove a theorem of Hashimoto [Tokyo J. Math. 23 (2000), 137–159] giving an intrinsic characterization of pseudoholomorphic curves in S6 and (beyond Hashimoto's work) S5. Instead of the Maurer–Cartan equations we use an embedding theorem into homogeneous spaces (here: S6=G2/SU3) involving the canonical connection.

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Metadaten
Author:Jost-Hinrich EschenburgGND, Theodoros Vlachos
URN:urn:nbn:de:bvb:384-opus4-685147
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/68514
ISSN:1669-9637OPAC
ISSN:0041-6932OPAC
Parent Title (Spanish):Revista de la Unión Matemática Argentina
Publisher:Union Matematica Argentina
Place of publication:Buenos Aires
Type:Article
Language:English
Year of first Publication:2019
Publishing Institution:Universität Augsburg
Release Date:2020/01/14
Tag:General Mathematics
Volume:60
Issue:2
First Page:517
Last Page:537
DOI:https://doi.org/10.33044/revuma.v60n2a16
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Differentialgeometrie
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):CC-BY 4.0: Creative Commons: Namensnennung (mit Print on Demand)