On automorphism groups of toroidal circle planes

TL;DR

This paper extends Schenkel's results on automorphism groups from flat Minkowski planes to toroidal circle planes, analyzing their structure and dimensions.

Contribution

It generalizes existing theorems about automorphism groups to the setting of toroidal circle planes, providing new insights into their symmetry properties.

Findings

Automorphism groups of toroidal circle planes are Lie groups.

Bound on the dimension of automorphism groups is established.

Characterization of planes with large automorphism groups.

Abstract

Schenkel proved that the automorphism group of a flat Minkowski plane is a Lie group of dimension at most 6 and described planes whose automorphism group has dimension at least 4 or one of whose kernels has dimension 3. We extend these results to the case of toroidal circle planes.