A complex orthogonal (geometric) structure on a complex manifold is a geometric structure locally modelled on a non-degenerate quadric. One of the first examples of such a structure on a compact manifold of dimension three was constructed by Guillot. In this paper, we show that the same manifold carries a family of uniformizable complex orthogonal (geometric) structures which includes Guillot’s structure; here, a structure is said to be uniformizable if it is a quotient of an invariant open set of a quadric by a Kleinian group. We also construct a family of uniformizable complex (geometric) projective structures on a related compact complex manifold of dimension three.

中文翻译：

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3维的复杂正交几何结构

甲复正交（几何）结构上的复杂的歧管是局部地仿照非退化二次几何结构。Guillot在尺寸为3的紧凑型歧管上构造这种结构的第一个示例之一。在本文中，我们表明同一流形带有一族可化的复杂正交（几何）结构，其中包括Guillot结构。此处，如果结构是二次方程的不变开集与克莱因组的商，则该结构被认为是可均匀化的。我们还在三维的相关紧致复杂流形上构造了一组可均匀化的复杂（几何）投影结构。