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arXiv · 1809.06953

Complex orthogonal geometric structures of dimension three

Mayra Méndez
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Abstract

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.

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Mayra Méndez. 2018-09-18. Complex orthogonal geometric structures of dimension three. https://arxiv.org/abs/1809.06953

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