Geometry of symmetric spaces of type EVI

TL;DR

This paper extends the geometric analysis of symmetric spaces of type EVI to arbitrary characteristic zero fields, linking point configurations to symplectic ternary algebra classifications.

Contribution

It generalizes Atsuyama's results to broader fields and connects geometric configurations with algebraic structures like Freudenthal triple systems.

Findings

Extended geometric classification to arbitrary characteristic zero fields.

Connected point configurations with symplectic ternary algebra classifications.

Provided new insights into the structure of symmetric spaces of type EVI.

Abstract

We generalize Atsuyama's result on the geometry of symmetric spaces of type EVI to the case of arbitrary field of characteristic zero. We relate the possible mutual positions of two points with the classification of balanced symplectic ternary algebras (also known as Freudenthal triple systems).