Complex orthogonal geometric structures of dimension three

Mayra Méndez ^[1]
1. [1] Universidad Autónoma del Estado de Morelos
  
  Universidad Autónoma del Estado de Morelos
  
  México
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 36, Nº 6, 2020, págs. 1721-1752
Idioma: inglés
DOI: 10.4171/rmi/1181
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Resumen
- 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.