Elliptic, Hyperbolic, Pseudoelliptic, and Pseudohyperbolic Geometries

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


In 0.8.8 we have seen that the groups of rotations of hyperspheres in the real Euclidean and pseudo-Euclidean spaces R n+1 and R n+1 are imprimitive and that the classes of primitivity of these hyperspheres are pairs of their antipodal points. Therefore, if we identify pairs of antipodal points of these hyperspheres we obtain homogeneous spaces with primitive groups of transformations.


Sectional Curvature Hyperbolic Space Hyperbolic Geometry Cross Ratio Regular Polyhedron 
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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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