{"title":"The moduli space of flat maximal space-like embeddings in pseudo-hyperbolic space","authors":"Nicholas Rungi, Andrea Tamburelli","doi":"10.1007/s10455-025-09994-z","DOIUrl":null,"url":null,"abstract":"<div><p>We study the moduli space of flat maximal space-like embeddings in <span>\\({\\mathbb {H}}^{2,2}\\)</span> 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.\n</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":"67 3","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10455-025-09994-z.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Global Analysis and Geometry","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10455-025-09994-z","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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.
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.
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