Grassmannians of lines defined in the geometry of a pseudo-polarity

TL;DR

This paper introduces a new regular point-line geometry based on pseudo-polarity, explores its automorphism group, and relates it to the geometry of regular lines and planes, expanding the understanding of pseudo-polarity geometries.

Contribution

It defines a weaker regular point-line geometry in pseudo-polarity context and determines its automorphism group, linking it to regular lines and planes.

Findings

Automorphism group of the geometry is explicitly determined.

The geometry is weaker than the metric-projective geometry.

The structure can be expressed via regular lines and planes.

Abstract

The regular point-line geometry with respect to a pseudo-polarity is introduced. It is weaker than the underlying metric-projective geometry. The automorphism group of this geometry is determined. This geometry can be also expressed as the geometry of regular lines and planes.