The moduli space of flat maximal space-like embeddings in pseudo-hyperbolic space

We study the moduli space of flat maximal space-like embeddings in H2,2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {H}}<^>{2,2}$$\end{document} from various aspects. We first describe the associated Codazzi tensors to the embedding in the general setting, and then, we introduce a family of pseudo-K & auml;hler metrics on the moduli space. We show the existence of two Hamiltonian actions with associated moment maps and use them to find a geometric global Darboux frame for any symplectic form in the above family.