高度连通的7流形和非负截面曲率

IF 8.3 2区材料科学 Q1 MATERIALS SCIENCE, MULTIDISCIPLINARY ACS Applied Materials & Interfaces Pub Date : 2020-01-01 DOI:10.4007/annals.2020.191.3.3

S. Goette, M. Kerin, K. Shankar

{"title":"高度连通的7流形和非负截面曲率","authors":"S. Goette, M. Kerin, K. Shankar","doi":"10.4007/annals.2020.191.3.3","DOIUrl":null,"url":null,"abstract":"Summary: In this article, a six-parameter family of highly connected 7 -manifolds which admit an SO (3) invariant metric of non-negative sectional curvature is constructed and the Eells-Kuiper invariant of each is computed. In particular, it follows that all exotic spheres in dimension 7 admit an SO (3) -invariant metric of non-negative curvature.","PeriodicalId":5,"journal":{"name":"ACS Applied Materials & Interfaces","volume":null,"pages":null},"PeriodicalIF":8.3000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"26","resultStr":"{\"title\":\"Highly connected 7-manifolds and non-negative sectional curvature\",\"authors\":\"S. Goette, M. Kerin, K. Shankar\",\"doi\":\"10.4007/annals.2020.191.3.3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Summary: In this article, a six-parameter family of highly connected 7 -manifolds which admit an SO (3) invariant metric of non-negative sectional curvature is constructed and the Eells-Kuiper invariant of each is computed. In particular, it follows that all exotic spheres in dimension 7 admit an SO (3) -invariant metric of non-negative curvature.\",\"PeriodicalId\":5,\"journal\":{\"name\":\"ACS Applied Materials & Interfaces\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":8.3000,\"publicationDate\":\"2020-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"26\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Materials & Interfaces\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4007/annals.2020.191.3.3\",\"RegionNum\":2,\"RegionCategory\":\"材料科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATERIALS SCIENCE, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Materials & Interfaces","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4007/annals.2020.191.3.3","RegionNum":2,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATERIALS SCIENCE, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 26

摘要

摘要:构造了具有非负截面曲率的SO(3)不变度量的六参数高连通7流形族，并计算了它们的Eells-Kuiper不变量。特别地，可以得出，所有在7维的奇异球都有一个非负曲率的SO(3)不变度规。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Highly connected 7-manifolds and non-negative sectional curvature

Summary: In this article, a six-parameter family of highly connected 7 -manifolds which admit an SO (3) invariant metric of non-negative sectional curvature is constructed and the Eells-Kuiper invariant of each is computed. In particular, it follows that all exotic spheres in dimension 7 admit an SO (3) -invariant metric of non-negative curvature.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

ACS Applied Materials & Interfaces 工程技术-材料科学：综合

CiteScore

16.00

自引率

6.30%

发文量

4978

审稿时长

1.8 months

期刊介绍： ACS Applied Materials & Interfaces is a leading interdisciplinary journal that brings together chemists, engineers, physicists, and biologists to explore the development and utilization of newly-discovered materials and interfacial processes for specific applications. Our journal has experienced remarkable growth since its establishment in 2009, both in terms of the number of articles published and the impact of the research showcased. We are proud to foster a truly global community, with the majority of published articles originating from outside the United States, reflecting the rapid growth of applied research worldwide.