Affinely equivalent complete flat manifolds

Author: Michalstrok Sadowski

Source: Central European Journal of Mathematics, Volume 2, Number 2, 1 April 2004 , pp. 332-338(7)

Publisher: Central European Science Journals

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Abstract:

Let EAff(Gamma, G, m) be the set of affine equivalence classes of m-dimensional complete flat manifolds with a fixed fundamental group Gamma and a fixed holonomy group G. Let n be the dimension of a closed flat manifold whose fundamental group is isomorphic to Gamma. We describe EAff(Gamma, G, m) in terms of equivalence classes of pairs (epsi,rho), consisting of epimorphisms of Gamma onto G and representations of G in Rm-n. As an application we give some estimates of card EAff(Gamma, G, m).

Keywords: COMPETE FLAT MANIFOLD; AFFINE DIFFEOMORPHISM; HOLONOMY GROUP; MSC (2000): PRIMARY: 53C99; SECONDARY: 53C25

Document Type: Research article

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