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 ℝm-n. As an application we give some estimates of card E Aff(Γ,G, m).
@article{bwmeta1.element.doi-10_2478_BF02476546,
author = {Michal Sadowski},
title = {Affinely equivalent complete flat manifolds},
journal = {Open Mathematics},
volume = {2},
year = {2004},
pages = {332-338},
zbl = {1110.53026},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02476546}
}
Michal Sadowski. Affinely equivalent complete flat manifolds. Open Mathematics, Tome 2 (2004) pp. 332-338. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02476546/
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