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Harmonic surfaces in the Cayley plane
Author(s) -
Correia N.,
Pacheco R.,
Svensson M.
Publication year - 2021
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms.12376
Subject(s) - twistor theory , mathematics , nilpotent , submanifold , pure mathematics , grassmannian , linear subspace , representation theory , harmonic map , riemann surface , harmonic , space (punctuation) , plane (geometry) , twistor space , algebra over a field , mathematical analysis , geometry , physics , quantum mechanics , computer science , operating system
We consider the twistor theory of nilconformal harmonic maps from a Riemann surface into the Cayley plane O P 2 = F 4 / Spin ( 9 ) . By exhibiting this symmetric space as a submanifold of the Grassmannian of 10‐dimensional subspaces of the fundamental representation of F 4 , techniques and constructions similar to those used in earlier works on twistor constructions of nilconformal harmonic maps into classical Grassmannians can also be applied in this case. The originality of our approach lies on the use of the classification of nilpotent orbits in Lie algebras as described by Djoković.