A construction of non--flat non--homogeneous symmetric parabolic geometries

TL;DR

This paper presents a series of constructed examples of non-flat, non-homogeneous parabolic geometries that possess a symmetry at every point, expanding understanding of symmetric structures in complex geometric contexts.

Contribution

The paper introduces a novel construction method for non-flat, non-homogeneous symmetric parabolic geometries, providing new examples in the field.

Findings

Constructed explicit examples of non-flat, non-homogeneous symmetric parabolic geometries.

Demonstrated the existence of geometries with pointwise symmetries that are not homogeneous.

Expanded the class of known symmetric parabolic geometries.

Abstract

We construct a series of examples of non--flat non--homogeneous parabolic geometries that carry a symmetry of the parabolic geometry at each point.