{"title":"平面整体的刚性","authors":"GÉRARD BESSON, GILLES COURTOIS, SA’AR HERSONSKY","doi":"10.1017/etds.2024.58","DOIUrl":null,"url":null,"abstract":"We prove that the existence of one horosphere in the universal cover of a closed Riemannian manifold of dimension <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000580_inline1.png\"/> <jats:tex-math> $n \\geq 3$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> with strongly <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000580_inline2.png\"/> <jats:tex-math> $1/4$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-pinched or relatively <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000580_inline3.png\"/> <jats:tex-math> $1/2$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-pinched sectional curvature, on which the stable holonomy along one horosphere coincides with the Riemannian parallel transport, implies that the manifold is homothetic to a real hyperbolic manifold.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Rigidity of flat holonomies\",\"authors\":\"GÉRARD BESSON, GILLES COURTOIS, SA’AR HERSONSKY\",\"doi\":\"10.1017/etds.2024.58\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that the existence of one horosphere in the universal cover of a closed Riemannian manifold of dimension <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" mime-subtype=\\\"png\\\" xlink:href=\\\"S0143385724000580_inline1.png\\\"/> <jats:tex-math> $n \\\\geq 3$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> with strongly <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" mime-subtype=\\\"png\\\" xlink:href=\\\"S0143385724000580_inline2.png\\\"/> <jats:tex-math> $1/4$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-pinched or relatively <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" mime-subtype=\\\"png\\\" xlink:href=\\\"S0143385724000580_inline3.png\\\"/> <jats:tex-math> $1/2$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-pinched sectional curvature, on which the stable holonomy along one horosphere coincides with the Riemannian parallel transport, implies that the manifold is homothetic to a real hyperbolic manifold.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/etds.2024.58\",\"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://doi.org/10.1017/etds.2024.58","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We prove that the existence of one horosphere in the universal cover of a closed Riemannian manifold of dimension $n \geq 3$ with strongly $1/4$ -pinched or relatively $1/2$ -pinched sectional curvature, on which the stable holonomy along one horosphere coincides with the Riemannian parallel transport, implies that the manifold is homothetic to a real hyperbolic manifold.
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