Euclidean, Pseudo-Euclidean, Conformal and Pseudoconformal Geometries

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

Abstract

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.

Keywords

Great Circle Conformal Transformation Fractional Linear Transformation Steiner Triple System Real Plane 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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