Geodesic
Cut and Paste in 2-Dimensional Projective Planes and Circle Planes
Canadian mathematical bulletin, Tome 38 (1995) no. 4, pp. 469-480

Voir la notice de l'article provenant de la source Cambridge University Press

We describe two methods to combine sets of lines of different 2-dimensional projective planes into line sets of new 2-dimensional projective planes. Using these methods we describe several ways in which sets of circles of different 2-dimensional circle planes can be combined into circle sets of new 2-dimensional circle planes.
DOI : 10.4153/CMB-1995-069-1
Mots-clés : 51H10, 51H15, 51B10, 51B15, 51B20 
Polster, B. Cut and Paste in 2-Dimensional Projective Planes and Circle Planes. Canadian mathematical bulletin, Tome 38 (1995) no. 4, pp. 469-480. doi: 10.4153/CMB-1995-069-1
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[1] 1. Artzy, R. and Groh, H., Laguerre and Minkowski planes produced by dilatations, J. Geom. 26(1986), 1—20. Google Scholar

[2] 2. Buchanan, T., Hähl, H. and Löwen, R., Topologische Ovale, Geom. Dedicata 9(1980), 401–424. Google Scholar

[3] 3. Groh, H., Topologische Laguerreebenen I, Abh. Math. Sem. Univ. Hamburg 32(1968), 216–231. Google Scholar

[4] 4. Groh, H., Topologische Laguerreebenen II, Abh. Math. Sem. Univ. Hamburg 34( 1970), 11—21. Google Scholar

[5] 5. Groh, H., Laguerre planes generated by Moebius planes, Abh. Math. Sem. Univ. Hamburg 40(1974), 43—63. Google Scholar

[6] 6. Groh, H., Flat Moebius and Laguerre planes, Abh. Math. Sem. Univ. Hamburg 40(1974), 64–76. Google Scholar

[7] 7. Groh, H., Ovals and non-ovoidal Laguerre planes, J. Reine Angew. Math. 267(1974), 50–66. Google Scholar

[8] 8. Hartmann, E., Eine Klasse nicht einbettbarer Laguerre-Ebenen, J. Geom. 13(1979), 49–67. Google Scholar

[9] 9. Hartmann, E., Beispiele nicht einbettbarer reeller Minkowski-Ebenen, Geom. Dedicata 10(1981), 155—159. Google Scholar

[10] 10. Hilbert, D., Grundlagen der Géométrie, Teubner, Leipzig, 1899. Google Scholar

[11] 11. Hilbert, D., Grundlagen der Géométrie, 8th ed.,Teubner, Stuttgart, 1956. Google Scholar

[12] 12. Löwen, R. and Pfüller, U., Two-dimensional Laguerre planes over convex functions, Geom. Dedicata 23 (1987), 73–85. Google Scholar

[13] 13. Moulton, F. R., A simple non-desarguesian plane Geometry, Trans. Amer. Math. Soc. 3(1902), 192—195. Google Scholar

[14] 14. Munkres, J. R., Topology—a first course, Prentice-Hall, New Jersey, 1975. Google Scholar

[15] 15. Pierce, W. A., Moulton planes, Canad. J. Math. 13(1961), 427–436. Google Scholar

[16] 16. Pierce, W. A., Collineations of affine Moulton planes, Canad. J. Math. 16(1964), 46–62. Google Scholar

[17] 17. Pierce, W. A., Collineations of projective Moulton planes, Canad. J. Math. 16(1964), 637–656. Google Scholar

[18] 18. Polster, B. and Steinke, G. F., Criteria for two-dimensional circle planes, Beitràge Algebra Geom. 35(1994), 181–191. Google Scholar

[19] 19. Salzmann, H., Topological planes, Adv. Math. 2(1967), 1–60. Google Scholar

[20] 20. Schenkel, A., Topologische Minkowski-Ebenen, Dissertation, Erlangen-Nurnberg, 1980. Google Scholar

[21] 21. Steinke, G. F., Topological affine planes composed of two Desarguesian halfplanes and projective planes with trivial collineation group, Arch. Math. 44(1985), 472–480. Google Scholar

[22] 22. Steinke, G. F., A family of 2-dimensional Minkowski planes with small automorphism groups, Results Math. 26(1994), 131–142. Google Scholar

[23] 23. Stroppel, M., A note on Hilbert and Beltrami systems, Results Math. 24(1993), 342–347. Google Scholar

[24] 24. Wölk, D., Topologische Möbiusebenen, Math. Z. 93(1966), 311–333 Google Scholar

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