Euclidean, Pseudo-Euclidean, Conformal and Pseudoconformal Geometries

  • Boris Rosenfeld
Part of the Mathematics and Its Applications book series (MAIA, volume 393)


In 0.5.3 we have defined the real Euclidean space R n as the affine space E n whose vectors satisfy axioms E.1° – 5°. Since the inner product x 2 of a vector x = x 2 e i of this space by itself is a positive definite quadratic form x 2 = e ij x i x j , this space is also called a quadratic Euclidean space. In 0.5.3 we have seen that the space R n also satisfies the axioms M.1° – 3° of a metric space.


Great Circle Conformal Transformation Fractional Linear Transformation Steiner Triple System Real Plane 
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Copyright information

© Springer Science+Business Media Dordrecht 1997

Authors and Affiliations

  • Boris Rosenfeld
    • 1
  1. 1.Department of MathematicsPennsylvania State UniversityUniversity ParkUSA

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