Elliptic, Hyperbolic, Pseudoelliptic, and Pseudohyperbolic Geometries
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 ℓ 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.
KeywordsSectional Curvature Hyperbolic Space Hyperbolic Geometry Cross Ratio Regular Polyhedron
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