Affinely equivalent complete flat manifolds |
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Authors: | Michal Sadowski |
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Institution: | (1) Department of Mathematics, University of Gdańsk, 80-952 Gdańsk Wita Stwosza 57, Poland |
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Abstract: | Let E
Aff(Γ,G, m) be the set of affine equivalence classes of m-dimensional complete flat manifolds with a fixed fundamental group Γ and a fixed holonomy group G. Let n be the dimension of a closed flat manifold whose fundamental group is isomorphic to Γ. We describe E
Aff(Γ,G, m) in terms of equivalence classes of pairs (ε, ρ), consisting of epimorphisms of Γ onto G and representations of G in ℝ
m-n
. As an application we give some estimates of card E
Aff(Γ,G, m). |
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Keywords: | Compete flat manifold affine diffeomorphism holonomy group |
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