{"title":"Variation formulae for the volume of coassociative submanifolds","authors":"Tommaso Pacini, Alberto Raffero","doi":"10.1007/s10455-024-09955-y","DOIUrl":null,"url":null,"abstract":"<div><p>We prove new variation formulae for the volume of coassociative submanifolds, expressed in terms of <span>\\(G_2\\)</span> data. These formulae highlight the role of the ambient torsion and Ricci curvature. As a special case, we obtain a second variation formula for variations within the moduli space of coassociative submanifolds. These results apply, for example, to coassociative fibrations. We illustrate our formulae with several examples, both homogeneous and non.\n</p></div>","PeriodicalId":8268,"journal":{"name":"Annals of Global Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","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/s10455-024-09955-y","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 prove new variation formulae for the volume of coassociative submanifolds, expressed in terms of \(G_2\) data. These formulae highlight the role of the ambient torsion and Ricci curvature. As a special case, we obtain a second variation formula for variations within the moduli space of coassociative submanifolds. These results apply, for example, to coassociative fibrations. We illustrate our formulae with several examples, both homogeneous and non.
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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