{"title":"The space of closed G2-structures. I. Connections","authors":"Pengfei Xu, Kai Zheng","doi":"10.1093/qmath/haae004","DOIUrl":null,"url":null,"abstract":"In this article, we develop foundational theory for geometries of the space of closed G2-structures in a given cohomology class as an infinite-dimensional manifold. We construct Levi-Civita connections for Sobolev-type metrics, formulate geodesic equations and analyze the variational structures of torsion-free G2-structures under these Sobolev-type metrics.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":"160 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quarterly Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1093/qmath/haae004","RegionNum":4,"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
In this article, we develop foundational theory for geometries of the space of closed G2-structures in a given cohomology class as an infinite-dimensional manifold. We construct Levi-Civita connections for Sobolev-type metrics, formulate geodesic equations and analyze the variational structures of torsion-free G2-structures under these Sobolev-type metrics.
期刊介绍：
The Quarterly Journal of Mathematics publishes original contributions to pure mathematics. All major areas of pure mathematics are represented on the editorial board.
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