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.

中文翻译：

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黎曼双曲线化

查尼和戴维斯的严格双曲线化过程产生了大量且丰富的负弯曲空间（在测地线意义上）。该过程基于 Gromov 引入的早期版本，后来由 Davis 和 Januszkiewicz 研究。如果 M 是一个流形，那么它的查尼-戴维斯严格双曲线化也是一个流形，但是所获得的负曲线度量远非黎曼度量，因为它具有大量且复杂的奇点集。我们证明这些奇点可以被消除（假设超醇化部分很大）。因此，严格的双曲线化过程可以在黎曼设置中完成。