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

IF 0.6 3区数学 Q3 MATHEMATICS

Annals of Global Analysis and Geometry Pub Date : 2025-04-03 DOI:10.1007/s10455-025-09994-z

Nicholas Rungi, Andrea Tamburelli

引用次数: 0

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-Kähler 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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伪双曲空间中平面极大类空嵌入的模空间

我们从各个方面研究了\({\mathbb {H}}^{2,2}\)中平面极大类空嵌入的模空间。我们首先在一般情况下描述与嵌入相关的Codazzi张量，然后在模空间上引入pseudo-Kähler度量族。我们证明了两个具有相关矩映射的哈密顿作用的存在性，并利用它们找到了上述族中任何辛形式的几何全局达布坐标系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Global Analysis and Geometry 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal examines global problems of geometry and analysis as well as the interactions between these fields and their application to problems of theoretical physics. It contributes to an enlargement of the international exchange of research results in the field. The areas covered in Annals of Global Analysis and Geometry include: global analysis, differential geometry, complex manifolds and related results from complex analysis and algebraic geometry, Lie groups, Lie transformation groups and harmonic analysis, variational calculus, applications of differential geometry and global analysis to problems of theoretical physics.