JournalsrmiVol. 36, No. 6pp. 1721–1752

Complex orthogonal geometric structures of dimension three

  • Mayra Méndez

    Universidad Autónoma del Estado de Morelos (UAEM), Cuernavaca, Mexico
Complex orthogonal geometric structures of dimension three cover

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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.

Cite this article

Mayra Méndez, Complex orthogonal geometric structures of dimension three. Rev. Mat. Iberoam. 36 (2020), no. 6, pp. 1721–1752

DOI 10.4171/RMI/1181