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On motion groups of locally Lobachevskijan three-dimensional manifolds. (Russian) Zbl 0669.51012
First the authors give definitions of the n-dimensional manifold of constant negative curvature and the discrete group of motions of a space \(X^ n\) (where \(X^ n\) is \(E^ n\), \(S^ n\) or \(\Lambda^ n)\) and consider their basic relations. Using the prismatic manifolds in \(\Lambda^ 3\) they investigate motion groups for manifolds with locally Lobachevskijan metric. They define the group of symmetries of the 4p- angles prism. It is verified the preservation of the identification by generators such a group and by generators of all its subgroups and motions disturbing identification are step-by-step rejected. It is also proved that the leaving motions preserve the identification pointwisely.
Reviewer: P.Burda

MSC:
51H20 Topological geometries on manifolds
51M20 Polyhedra and polytopes; regular figures, division of spaces
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