Complex orthogonal geometric structures of dimension three
Differential Geometry
2018-09-20 v1
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
@article{arxiv.1809.06953,
title = {Complex orthogonal geometric structures of dimension three},
author = {Mayra Méndez},
journal= {arXiv preprint arXiv:1809.06953},
year = {2018}
}
Comments
23 pages