Twistor triangles in the period domain of complex tori

Abstract

We study the geometry of (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 algebras (of real dimension 8) generated by the complex structure operators J 1 , J 2 , J 3 . Considering the period domain as a homogeneous space for G = GL 4n (R), we introduce on it a G-invariant pseudometric and define pseudometric invariants, helping us (generally) to distinguish triangles from a reasonably defined class up to G-equivalence.