双曲三维流形的球面CR单值化
首发时间:2020-04-22
摘要:具有球面CR结构的3维流形一直是复双曲几何研究领域中一个有趣的课题,对于一般的三维流形,该问题是非常困难的。至今,只有极少数的双曲三维流形被证明具有球面CR单值化。本文我们证明了双曲三维流形m009 具有一个球面CR单值化结构,即m009与复双曲三角群(3,3,5,$\infty$)在无穷处的流形同胚。
关键词: 复双曲几何; Poincar\'e多面体定理; Dirichlet域; 无穷处的流形
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On uniformizable sphere CR structures of hyperbolic 3-manifolds
Abstract:\justifying The 3-manifolds that admit a spherical CR structure has always been a interesting project in complex hyperbolic geometry. This problem is very difficult for general three dimensional manifolds. So far, only a few hyperbolic 3-manifolds have been proved to admit a uniformizable spherical CR structure. We show that m009 admit a uniformizable spherical CR structure, i.e. the manifold at infinity of the complex hyperbolic (3,3,5,$\infty$)-triangle group is homeomorphic to the manifold m009.
Keywords: Complex hyperbolic geometry Poincar\'e polyhedron theorem Dirichlet domain The manifold at infinity
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