• Corpus ID: 236170909

Para-hyperK\"ahler geometry of the deformation space of maximal globally hyperbolic anti-de Sitter three-manifolds

@inproceedings{Mazzoli2021ParahyperKahlerGO,
  title={Para-hyperK\"ahler geometry of the deformation space of maximal globally hyperbolic anti-de Sitter three-manifolds},
  author={Filippo Mazzoli and Andrea Seppi and Andrea Tamburelli},
  year={2021}
}
In this paper we study the para-hyperK\"ahler geometry of the deformation space of MGHC anti-de Sitter structures on $\Sigma\times\mathbb R$, for $\Sigma$ a closed oriented surface. We show that a neutral pseudo-Riemannian metric and three symplectic structures coexist with an integrable complex structure and two para-complex structures, satisfying the relations of para-quaternionic numbers. We show that these structures are directly related to the geometry of MGHC manifolds, via the Mess… 
1 Citations

Pseudo-K\"ahler geometry of properly convex projective structures on the torus

In this paper we prove the existence of a pseudo-Kähler structure on the deformation space B0pT q of properly convex RP-structures over the torus. In particular, the pseudo-Riemannian metric and the