{"title":"Manifolds of positive Ricci curvature with quadratically asymptotically nonnegative curvature and infinite topological type","authors":"Huihong Jiang, Yihu Yang","doi":"10.4310/cag.2021.v29.n5.a7","DOIUrl":null,"url":null,"abstract":"We construct a complete n-dimensinal (n ≥ 6) Riemannian manifold of positive Ricci curvature with quadratically asymptotically nonnegative sectional curvature and infinite topological type. This gives a negative answer to a problem proposed by Jiping Sha and Zhongmin Shen [12] in the case of n ≥ 6.","PeriodicalId":50662,"journal":{"name":"Communications in Analysis and Geometry","volume":"1 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Analysis and Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/cag.2021.v29.n5.a7","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
Abstract
We construct a complete n-dimensinal (n ≥ 6) Riemannian manifold of positive Ricci curvature with quadratically asymptotically nonnegative sectional curvature and infinite topological type. This gives a negative answer to a problem proposed by Jiping Sha and Zhongmin Shen [12] in the case of n ≥ 6.
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