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Hyperbolic Geometry, Dimension-Free

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Non-Euclidean Geometries

Part of the book series: Mathematics and Its Applications ((MAIA,volume 581))

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Bibliography

  1. Benz, W.: A common characterization of euclidean and hyperbolic geometry by functional equations. Publ. Math. Debrecen 63 (2003) 495–510.

    MATH  MathSciNet  Google Scholar 

  2. Benz, W.: Hyperbolic distances in Hilbert Spaces. Aequat. Math. 58 (1999) 16–30.

    MATH  MathSciNet  Google Scholar 

  3. Benz, W.: Lie Sphere Geometry in Hilbert Spaces. Results Math. 40 (2001) 9–36.

    MATH  MathSciNet  Google Scholar 

  4. Benz, W.: Mappings preserving two hyperbolic distances. J. Geom. 70 (2001) 8–16.

    Article  MATH  MathSciNet  Google Scholar 

  5. Benz, W.: Möbius Sphere Geometry in Inner Product Spaces. Preprint: Aequat. Math. 66 (2003) 284–320.

    Google Scholar 

  6. Blunck, A., Havlicek, H.: Projective Representations 11. Generalized chain geometries. Abh. Math. Sem. Univ. Hamburg 70 (2000) 301–313.

    Article  MathSciNet  MATH  Google Scholar 

  7. Farrahi, B.: A characterization of isometries of absolute planes. Result. Math. 4 (1981) 34–38.

    MATH  MathSciNet  Google Scholar 

  8. Klotzek, B., Quaisser, E.: Nichteuklidische Geometrie. Deutscher Verlag der Wissenschaften. Berlin 1978.

    MATH  Google Scholar 

  9. Kuz’minyh, A.V.: Mappings preserving the distance 1. Sibirsk. Mat. Z. 20 (1979) 597–602.

    MathSciNet  Google Scholar 

  10. Molnár, E.: Kreisgeometrie und konforme Interpretation des mehrdimensionalen metrischen Raumes. Periodica Math. Hung. 10 (1979) 237–259.

    Article  MATH  Google Scholar 

  11. Nöbeling, G.: Einführung in die nichteuklidische Geometrie. de Gruyter. Berlin 1976.

    Google Scholar 

  12. Rédei, L.: Begründung der euklidischen und nichteuklidischen Geometrien. Akad. Kiadó. Budapest 1965.

    MATH  Google Scholar 

  13. Schröder, E.M.: Eine Ergänzung zum Satz von Beckman und Quarles. Aequat. Math. 19 (1979) 89–92.

    Article  MATH  Google Scholar 

  14. Wiegand, T.: A polar-coordinate model of the hyperbolic plane. Publ. Math. 41 (1992) 161–171.

    MATH  MathSciNet  Google Scholar 

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Benz, W. (2006). Hyperbolic Geometry, Dimension-Free. In: Prékopa, A., Molnár, E. (eds) Non-Euclidean Geometries. Mathematics and Its Applications, vol 581. Springer, Boston, MA. https://doi.org/10.1007/0-387-29555-0_4

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