On Minkowski planes with transitive groups of homotheties
In analogy with the well-known Lenz-Barlotti classification of projective planes, there are the Hering classification of Möbius planes [\textit{C. Hering}, Math. Z. 87, 252-262 (1965; Zbl 0126.166)], the Kleinewillinghofer classification of Laguerre planes [\textit{R. Kleinewillinghofer}, Arch. Math. 34, 469-480 (1980; Zbl 0457.51010)], and the Klein-Kroll classification of Minkowski planes [the authors, J. Geom. 36, No. 1/2, 99-109 (1989; Zbl 0694.51005)] which was later refined by the first author [J. Geom. 43, No. 1/2, 116-128 (1992; Zbl 0746.51009)]. A family \(M(r)\) of topological Minkowski planes was constructed by \textit{E. Hartmann} [Geom. Dedicata 10, 155-159 (1981; Zbl 0454.51004)]. A main result of the present work is that these planes \(M(r)\) of E. Hartmann (with \(r\) not 1) are completely characterized as the (necessarily infinite) locally compact, connected and finite dimensional Minkowski planes of class 19 (of the refined Klein-Kroll classification).
scientific article; zbMATH DE number 706679
scientific article