A geometric transition from hyperbolic to anti-de Sitter geometry
A geometric transition from hyperbolic to anti-de Sitter geometry
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从双曲几何到反德西特几何的几何过渡
DOI：
10.2140/gt.2013.17.3077
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发表时间：
2013
影响因子：
2
通讯作者：
J. Danciger
中科院分区：
文献类型：
--
作者：
J. Danciger
我们介绍了两个齐次三维几何：双曲几何和反德西特（AdS）几何之间的几何过渡。给出了一个三维双曲结构的路径，崩溃到一个双曲平面上，我们描述了一种方法，用于构建一个自然的延续这条路径到AdS结构。特别是当双曲锥流形坍缩时，在过渡的“另一边”产生的AdS流形具有快子奇点。该方法涉及一种新的过渡几何称为半管几何的研究。我们证明了这些方法的情况下，当流形是单位切丛的.2;m;m/三角orbifold m 5。
We introduce a geometric transition between two homogeneous three-dimensional geometries: hyperbolic geometry and anti-de Sitter (AdS) geometry. Given a path of three-dimensional hyperbolic structures that collapse down onto a hyperbolic plane, we describe a method for constructing a natural continuation of this path into AdS structures. In particular, when hyperbolic cone manifolds collapse, the AdS manifolds generated on the “other side” of the transition have tachyon singularities. The method involves the study of a new transitional geometry called half-pipe geometry. We demonstrate these methods in the case when the manifold is the unit tangent bundle of the .2;m;m/ triangle orbifold for m 5.