Harmonic surfaces in the Cayley plane
| Autor: | Rui Pacheco, N. Correia, Martin Svensson |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics 58E20 General Mathematics Riemann surface Harmonic map 53C43 (primary) 58E20 53C43 Twistor theory symbols.namesake Differential Geometry (math.DG) Grassmannian Symmetric space Cayley plane Lie algebra Fundamental representation symbols FOS: Mathematics Mathematics::Representation Theory Mathematics |
| Zdroj: | Correia, N, Pacheco, R & Svensson, M 2021, ' Harmonic surfaces in the Cayley plane ', Journal of the London Mathematical Society, vol. 103, no. 2, pp. 353-371 . https://doi.org/10.1112/jlms.12376 |
| DOI: | 10.1112/jlms.12376 |
| Popis: | We consider the twistor theory of nilconformal harmonic maps from a Riemann surface into the Cayley plane $\mathbf{O} P^2=F_4/\mathrm{Spin}(9)$. 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 D. Djokovi\'{c}. |
| Databáze: | OpenAIRE |
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