{"title":"On $$G_2$$ Manifolds with Cohomogeneity Two Symmetry","authors":"Benjamin Aslan, Federico Trinca","doi":"10.1007/s00220-024-05052-0","DOIUrl":null,"url":null,"abstract":"<p>We consider <span>\\({{\\,\\mathrm{G_2}\\,}}\\)</span> manifolds with a cohomogeneity two <span>\\({{\\,\\mathrm{\\mathbb {T}}\\,}}^2\\times {{\\,\\textrm{SU}\\,}}(2)\\)</span> symmetry group. We give a local characterization of these manifolds and we describe the geometry, including regularity and singularity analysis, of cohomogeneity one calibrated submanifolds in them. We apply these results to the manifolds recently constructed by Foscolo–Haskins–Nordström and to the Bryant–Salamon manifold of topology <span>\\(/\\!\\!\\!S(S^3)\\)</span>. In particular, we describe new large families of complete <span>\\({{\\,\\mathrm{\\mathbb {T}}\\,}}^2\\)</span>-invariant associative submanifolds in them.</p>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s00220-024-05052-0","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
We consider \({{\,\mathrm{G_2}\,}}\) manifolds with a cohomogeneity two \({{\,\mathrm{\mathbb {T}}\,}}^2\times {{\,\textrm{SU}\,}}(2)\) symmetry group. We give a local characterization of these manifolds and we describe the geometry, including regularity and singularity analysis, of cohomogeneity one calibrated submanifolds in them. We apply these results to the manifolds recently constructed by Foscolo–Haskins–Nordström and to the Bryant–Salamon manifold of topology \(/\!\!\!S(S^3)\). In particular, we describe new large families of complete \({{\,\mathrm{\mathbb {T}}\,}}^2\)-invariant associative submanifolds in them.
期刊介绍:
The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.