The combinatorial geometry of -Gorenstein quasi-homogeneous surface singularities

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• 作者：Anna Pratoussevitch^a ; ^{annap@liv.ac.uk"" rel=""nofollow}
• 关键词：Lorentz space form ; Polyhedral fundamental domain ; Quasi-homogeneous singularity
• 刊名：Differential Geometry and its Applications
• 出版年：2011
• 出版时间：August 2011
• 年：2011
• 卷：29
• 期：4
• 页码：507-515
• 全文大小：214 K

文摘

The main result of this paper is a construction of fundamental domains for certain group actions on Lorentz manifolds of constant curvature. We consider the simply connected Lie group . The Killing form on the Lie group gives rise to a bi-invariant Lorentz metric of constant curvature. We consider a discrete subgroup Γ₁ and a cyclic discrete subgroup Γ₂ in which satisfy certain conditions. We describe the Lorentz space form by constructing a fundamental domain for the action of Γ₁×Γ₂ on by (g,h)x=gxh⁻¹. This fundamental domain is a polyhedron in the Lorentz manifold with totally geodesic faces. For a co-compact subgroup Γ₁ the corresponding fundamental domain is compact.