Modified classical flat Minkowski planes
In this paper, the author continues the study begun in [Adv. Geom. 4, No. 3, 319--340 (2004; Zbl 1067.51008)] (a review in which one can find the definitions of the main concepts) of flat Minkowski planes whose automorphism groups are \(3\)-dimensional. New families of flat Minkowski planes that admit simple groups of automorphisms isomorphic to \(\mathrm{PSL}_2({\mathbb R})\) are described. The action of \(\mathrm{PSL}_2({\mathbb R})\) on the torus is the same as for the flat Minkowski planes in [loc. cit.] They are constructed by piecing together circles from the classical flat Minkowski plane. Their Klein-Kroll type is determined, and it turns out that they belong to Klein-Kroll types that are already known to exist.
scientific article; zbMATH DE number 6854805