We study the geometry of the (generalized) twistor triangles $\triangle J_1J_2J_3$ in the period domain of compact complex tori of complex dimension $2n$ by the means of the representation theory of the algebras (of real dimension 8) generated by the complex structures $J_1,J_2,J_3$. Considering the period domain as the homogeneous space for $G=GL_{4n}(\mathbb{R})$, we introduce on it a $G$-invariant pseudometric and define pseudometric invariants, helping us to distinguish triangles from a reasonable class up to $G$-equivalence.

中文翻译：

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复圆环周期域中的扭曲线

我们通过复数生成的代数（实维数为 8）的表示理论，研究了复维数为 $2n$ 的紧复数环的周期域中（广义）扭曲三角形 $\triangle J_1J_2J_3$结构 $J_1,J_2,J_3$。将周期域视为 $G=GL_{4n}(\mathbb{R})$ 的齐次空间，我们在其上引入了 $G$ 不变的伪度量并定义了伪度量不变量，帮助我们将三角形与合理的类区分开来高达 $G$-等价物。