{"title":"完全大地超曲面的有限性","authors":"Simion Filip, David Fisher, Ben Lowe","doi":"arxiv-2408.03430","DOIUrl":null,"url":null,"abstract":"We prove that a negatively curved analytic Riemannian manifold that contains\ninfinitely many totally geodesic hypersurfaces is isometric to an arithmetic\nhyperbolic manifold.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"79 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Finiteness of totally geodesic hypersurfaces\",\"authors\":\"Simion Filip, David Fisher, Ben Lowe\",\"doi\":\"arxiv-2408.03430\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that a negatively curved analytic Riemannian manifold that contains\\ninfinitely many totally geodesic hypersurfaces is isometric to an arithmetic\\nhyperbolic manifold.\",\"PeriodicalId\":501271,\"journal\":{\"name\":\"arXiv - MATH - Geometric Topology\",\"volume\":\"79 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Geometric Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.03430\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Geometric Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.03430","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We prove that a negatively curved analytic Riemannian manifold that contains
infinitely many totally geodesic hypersurfaces is isometric to an arithmetic
hyperbolic manifold.
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