Twistor triangles in the period domain of complex tori

Abstract

We study the geometry of the (generalized) twistor triangles $△J_1{J}_2{J}_3$ 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 $G=G{L}_{4n}(\mathbb{R})$, 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.

28 pages, 3 figures, an erroneous statement in the third theorem about the diffeomorphism types of the connected components of the fiber of the multiplication map has been corrected, the proof has been rewritten. Some general editing of the text