We consider the twistor theory of nilconformal harmonic maps from a Riemann surface into the Cayley plane $\mathbb{O}{P}^2=F_4/\mathrm{Spin}(9)$. 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 Djoković.

中文翻译：

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Cayley平面中的谐波表面

我们考虑从Riemann曲面到Cayley平面的零形谐波映射的扭曲理论 $\mathbb{Ø}{P}^{\mathrm{2个}}=F_4/\mathrm{旋转}（9）$。通过将这个对称空间展示为基本表示的10维子空间的Grassmannian的子流形$F_4$，在这种情况下，也可以应用与之前在将非共形谐波映射的扭曲构造转化为经典Grassmannian中使用的技术和构造相似的技术和构造。我们的方法的独创性在于使用Djoković描述的李代数中幂等轨道的分类。