An axiomatics for hyperbolic projective-metric planes in terms of lines and orthogonality

• Autorzy: Pambuccian V.
• Języki publikacji: EN

Abstrakty

EN

Hyperbolic projective-metric planes, first axiomatized by R. Lingenberg [7], are shown to be axiomatizable in terms of lines and orthogonality.

Słowa kluczowe

EN

hyperbolic projective-metric plane

PL

płaszczyzna hiperboliczna rzutowo-metryczna

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2004
• Tom: Vol. 52, nr 3
• Strony: 297--302
• Opis fizyczny: Bibliogr. 14 poz., rys.

Twórcy

autor

Pambuccian V.

Bibliografia

• [1] F. Bachmann, Aufbau der Geometrie aus dem Spiegelungsbegrff, 2. Auage. Springer, Berlin, 1973.
• [2] W. Benz, Geometrische Transformationen, BI Wissenschaftsverlag, Mannheim, 1992.
• [3] W. Benz und E. M. Schröder, Bestimmung der orthogonalitätstreuen Permutationen euklidischer Räume, Geom. Dedicata 21 (1986), 265-276.
• [4] H. Havlicek, On Plücker transformations of generalized elliptic spaces, Rend. Mat. Appl. (7) 15 (1995), 39-56.
• [5] -, A characteristic property of elliptic Plücker transformations, J. Geom. 58 (1997), 106-116.
• [6] R. Lingenberg, Vollständige metrische Ebenen, Abh. Math. Sem. Univ. Hamburg 48 (1979), 241-263.
• [7] -, Metric Planes and Metric Vector Spaces, Wiley, New York, 1979.
• [8] -, Hyperbolisch-metrische Ebenen mit freier Beweglichkeit, in: Symposia Mathematica 11 (Convegno di Geometria, INDAM, Rome, 1972), Academic Press, London, 1973, 397-412.
• [9] K. List, On orthogonality-preserving Plücker transformations of hyperbolic spaces, Abh. Math. Sem. Univ. Hamburg 70 (2000), 63-75.
• [10] -, Harmonic mappings and hyperbolic Plücker transformations, J. Geom. 70 (2001), 108-116.
• [11] V. Pambuccian, Aufbau der hyperbolischen Geometrie aus dem Geradenorthogonalitätsbegriff, Acta Math. Hungar. 101 (2003), 51-61.
• [12] -, Hyperbolic geometry in terms of point-reections or of line-orthogonality, Math. Pannon., to appear.
• [13] V. Pambuccian, K. Prażmowski and K. Sakowicz, Defining co-punctuality in terms of line-orthogonality in plane hyperbolic geometry, Acta Math. Hungar., submitted.
• [14] K. Sakowicz, Axiomatizability of the dual external hyperbolic plane, Master's thesis, Warsaw University, Białystok Branch, 1988 (in Polish).