Die Geometrien der ebenen Schnitte quadratischer Mengen

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F. BUEKENHOUT introduced in [4] the notion of the quadratic set in projective space as a common generalization of the quadrics and the ovoids. In this paper we give an axiomatic foundation of the so-called “quadratic geometries”, i.e. the geometries of plane-sections of a quadratic set in an at least three-dimensional projective space, analogous to the concept of the Benz-planes i.e. the Mobius-, Laguerre-, or Minkowski-planes.