Riemannian hyperbolization
Riemannian hyperbolization
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DOI：
10.1007/s10240-020-00113-1
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发表时间：
2014-06
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影响因子：
--
通讯作者：
P. Ontaneda
中科院分区：
文献类型：
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作者：
P. Ontaneda
查尼和戴维斯的严格双曲化过程产生了大量的负曲空间（在测地线意义上）。这个过程是基于格罗莫夫提出的早期版本，后来由戴维斯和雅努什凯维奇研究。如果M是一个流形，它的Charney-Davis严格双曲化也是一个流形，但得到的负曲度量与黎曼度量相差甚远，因为它有一个大而复杂的奇点集。我们表明，这些奇点可以被删除（hyperolization片是大的）。因此，严格的双曲化过程可以在黎曼设置中完成。
The strict hyperbolization process of Charney and Davis produces a large and rich class of negatively curved spaces (in the geodesic sense). This process is based on an earlier version introduced by Gromov and later studied by Davis and Januszkiewicz. If M is a manifold its Charney-Davis strict hyperbolization is also a manifold, but the negatively curved metric obtained is very far from being Riemannian because it has a large and complicated set of singularities. We show that these singularities can be removed (provided the hyperolization piece is large). Hence the strict hyperbolization process can be done in the Riemannian setting.