DEFORMATION SPACES OF 3-DIMENSIONAL FLAT MANIFOLDS

Title & Authors
DEFORMATION SPACES OF 3-DIMENSIONAL FLAT MANIFOLDS
Kang, Eun-Sook; Kim, Ju-Young;

Abstract
The deformation spaces of the six orientable 3-dimensional flat Riemannian manifolds are studies. It is proved that the Teichmuller spaces are homeomorphic to the Euclidean spaces. To state more precisely, let $\small{\Phi}$ denote the holonomy group of the manifold. Then the Teichmuller space is homeomorphic to (1) $\small{{\mathbb{R}}^6\;if\;\Phi}$ is trivial, (2) $\small{{\mathbb{R}}^4\;if\;\Phi}$ is cyclic with order two, (3) $\small{{\mathbb{R}}^2\;if\;\Phi}$ is cyclic of order 3, 4 or 6, and (4) $\small{{\mathbb{R}}^3\;if\;\Phi\;\cong\;{\mathbb{Z}_2}\;\times\;{\mathbb{Z}_2}}$.
Keywords
Weil space;Teichmuller space;Bieberbach group;
Language
English
Cited by
References
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Spaces of Constant Curvature,