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Published in:
2007 | OriginalPaper | Chapter
δ-Projective Mappings, Isomorphism Theorems
Published in: Classical Geometries in Modern Contexts
Publisher: Birkhäuser Basel
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Let (
X, δ
) and (
V, ɛ
) be arbitrary real inner product spaces each containing at least two linearly independent elements. However, as in the earlier chapters we do not exclude the case that there exist infinite linearly independent subsets of
X
or
V
. One of the important results of this chapter is that the hyperbolic geometries (
X, M
(
X
)), (
V, M
(
V
)) over
X
= (
X, δ
),
V
= (
V, ɛ
), respectively,
M
the group of hyperbolic motions, are isomorphic (see p. 16f) if, and only if, (
X, δ
) and (
V, ɛ
) are isomorphic (see p. 1f).