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Cut and Paste in 2-Dimensional Projective Planes and Circle Planes

Published online by Cambridge University Press:  20 November 2018

B. Polster and
G. F. Steinke
B. Polster
Affiliation:
Department of Mathematics, University of Canterbury, Christchurch, New Zealand
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Abstract

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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.

Keywords

51H1051H1551B1051B1551B20

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 4 , 01 December 1995, pp. 469 - 480
Copyright
Copyright © Canadian Mathematical Society 1995

References

1. Artzy, R. and Groh, H., Laguerre and Minkowski planes produced by dilatations, J. Geom. 26(1986), 1—20.Google Scholar
2. Buchanan, T., Hähl, H. and Löwen, R., Topologische Ovale, Geom. Dedicata 9(1980), 401–424.Google Scholar
3. Groh, H., Topologische Laguerreebenen I, Abh. Math. Sem. Univ. Hamburg 32(1968), 216–231.Google Scholar
4. Groh, H., Topologische Laguerreebenen II, Abh. Math. Sem. Univ. Hamburg 34( 1970), 11—21.Google Scholar
5. Groh, H., Laguerre planes generated by Moebius planes, Abh. Math. Sem. Univ. Hamburg 40(1974), 43—63.Google Scholar
6. Groh, H., Flat Moebius and Laguerre planes, Abh. Math. Sem. Univ. Hamburg 40(1974), 64–76.Google Scholar
7. Groh, H., Ovals and non-ovoidal Laguerre planes, J. Reine Angew. Math. 267(1974), 50–66.Google Scholar
8. Hartmann, E., Eine Klasse nicht einbettbarer Laguerre-Ebenen, J. Geom. 13(1979), 49–67.Google Scholar
9. Hartmann, E., Beispiele nicht einbettbarer reeller Minkowski-Ebenen, Geom. Dedicata 10(1981), 155—159.Google Scholar
10. Hilbert, D., Grundlagen der Géométrie, Teubner, Leipzig, 1899.Google Scholar
11. Hilbert, D., Grundlagen der Géométrie, 8th ed.,Teubner, Stuttgart, 1956.Google Scholar
12. Löwen, R. and Pfüller, U., Two-dimensional Laguerre planes over convex functions, Geom. Dedicata 23 (1987), 73–85.Google Scholar
13. Moulton, F. R., A simple non-desarguesian plane Geometry, Trans. Amer. Math. Soc. 3(1902), 192—195.Google Scholar
14. Munkres, J. R., Topology—a first course, Prentice-Hall, New Jersey, 1975.Google Scholar
15. Pierce, W. A., Moulton planes, Canad. J. Math. 13(1961), 427–436.Google Scholar
16. Pierce, W. A., Collineations of affine Moulton planes, Canad. J. Math. 16(1964), 46–62.Google Scholar
17. Pierce, W. A., Collineations of projective Moulton planes, Canad. J. Math. 16(1964), 637–656.Google Scholar
18. Polster, B. and Steinke, G. F., Criteria for two-dimensional circle planes, Beitràge Algebra Geom. 35(1994), 181–191.Google Scholar
19. Salzmann, H., Topological planes, Adv. Math. 2(1967), 1–60.Google Scholar
20. Schenkel, A., Topologische Minkowski-Ebenen, Dissertation, Erlangen-Nurnberg, 1980.Google Scholar
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. Steinke, G. F., A family of 2-dimensional Minkowski planes with small automorphism groups, Results Math. 26(1994), 131–142.Google Scholar
23. Stroppel, M., A note on Hilbert and Beltrami systems, Results Math. 24(1993), 342–347.Google Scholar
24. Wölk, D., Topologische Möbiusebenen, Math. Z. 93(1966), 311–333 Google Scholar