On exceptional compact homogeneous geometries of type C3

TL;DR

This paper develops a unified approach to analyze exceptional compact homogeneous geometries of type C3, establishing their simple connectivity and determining their automorphism groups.

Contribution

It introduces a comprehensive framework for studying these geometries, proving their simple connectivity and computing their automorphism groups.

Findings

Proves these geometries are simply connected.

Calculates the full automorphism groups.

Provides a uniform framework for analysis.

Abstract

We provide a uniform framework to study the exceptional homogeneous compact geometries of type C3. This framework is then used to show that these are simply connected, answering a question by Kramer and Lytchak, and to calculate the full automorphism groups.