A fundamental theorem for dimension-free Möbius sphere geometries

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Erscheinungsjahr:
2008
Medientyp:
Text
Schlagworte:
  • Dimension-free geometry
  • Functional equation
  • Isomorphism of geometries
  • Möbius geometry of arbitrary (finite or infinite) dimension
  • Real inner product space
Beschreibung:
  • Let (X, δ) and (V, ε) be real inner product spaces of (finite or infinite) dimensions dim X, dim V greater than 1 (see our book [1] for special notions, results and the notation applied in the present paper). Especially the following Theorem 2 will be proved. The Möbius sphere geometries (X ∪ {∞}, double-struck M(X,δ)), (V ∪ {∞}, double-struck M(V,ε)) over (X,δ), (V,ε), respectively, where double-struck M is the Möbius group, are isomorphic (see [1], p. 16 f) if, and only if, (X,δ) ≅ (V,ε) (see [1], p. 1 f). © 2008 Birkhäuser Verlag AG.
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