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arXiv · 2310.12596

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

Nicholas Rungi·Andrea Tamburelli
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Abstract

We study the moduli space of flat maximal space-like embeddings in $\mathbb{H}^{2,2}$ 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\"ahler 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.

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Nicholas Rungi, Andrea Tamburelli. 2023-10-19. The moduli space of flat maximal space-like embeddings in pseudo-hyperbolic space. https://arxiv.org/abs/2310.12596

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