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Journal of Geometry

, Volume 16, Issue 1, pp 103–116 | Cite as

Über gemeinsame Lote Windschiefer geraden in elliptischen Räumen

  • H. R. Friedlein
Article

Abstract

Let the following motions in a projective elliptic space
(K,π) be called “normal forms”:Subspace-reflections, rotations, the product of a rotation and a point-reflection whose center lies on the axis of the rotation and the product of two rotations, whose axes of rotation are conjugated.
It is shown that all motions of
(K, π) have a normal-form provided any two lines of
(K, π) have a common perpendicular. The latter is true if and only if K is Pythagorean and if the polarity π can be represented by the unit-matrix.

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Literauturverzeichnis

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    AHRENS, J.: Begründung der absoluten Geometrie des Raumes aus dem Spiegelungsbegriff. Math. Z. 71. 154–185 (1959)CrossRefGoogle Scholar
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    BACHMANN, F.: Aufbau der Geometrie aus dem Spiegelungsbegriff. Berlin Heidelberg. New York 1973Google Scholar
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    EWALD, G.: Spiegelungsgeometrische Kennzeichnung euklidischer und nichteuklidischer Räume beliebiger Dimension. Abh. Math. Sem. Univ. Hamburg 41. 224–251 (1974)Google Scholar
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    EWALD, G.: über Bewegungen in der absoluten Geometrie. J. of Geometry 9. 49–56 (1977)Google Scholar

Copyright information

© Birkhäuser Verlag 1981

Authors and Affiliations

  • H. R. Friedlein
    • 1
  1. 1.Fachbereich 6 - MathematikUniversität EssenEssen

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