{"title":"g型结构的无扭连接","authors":"Brice Flamencourt","doi":"10.1016/j.difgeo.2023.102075","DOIUrl":null,"url":null,"abstract":"<div><p>We prove that for a Lie group <span><math><msub><mrow><mi>SO</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>R</mi><mo>)</mo><mo>⊂</mo><mi>G</mi><mo>⊂</mo><msub><mrow><mi>GL</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>R</mi><mo>)</mo></math></span>, any <em>G</em>-structure on a smooth manifold can be endowed with a torsion free connection which is locally the Levi-Civita connection of a Riemannian metric in a given conformal class. In this process, we classify the admissible groups.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Torsion-free connections on G-structures\",\"authors\":\"Brice Flamencourt\",\"doi\":\"10.1016/j.difgeo.2023.102075\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We prove that for a Lie group <span><math><msub><mrow><mi>SO</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>R</mi><mo>)</mo><mo>⊂</mo><mi>G</mi><mo>⊂</mo><msub><mrow><mi>GL</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>R</mi><mo>)</mo></math></span>, any <em>G</em>-structure on a smooth manifold can be endowed with a torsion free connection which is locally the Levi-Civita connection of a Riemannian metric in a given conformal class. In this process, we classify the admissible groups.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-11-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0926224523001018\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0926224523001018","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We prove that for a Lie group , any G-structure on a smooth manifold can be endowed with a torsion free connection which is locally the Levi-Civita connection of a Riemannian metric in a given conformal class. In this process, we classify the admissible groups.
分享
京公网安备 11010802042870号
京ICP备2023020795号-1
求助内容：
应助结果提醒方式：
扫码关注我们
