具有α-bach-flat的完全黎曼流形的刚性表征

IF 0.7 4区数学 Q2 MATHEMATICS

Journal of the Korean Mathematical Society Pub Date : 2021-01-01 DOI:10.4134/JKMS.J200086

Guangyue Huang, Qianyu Zeng

{"title":"具有α-bach-flat的完全黎曼流形的刚性表征","authors":"Guangyue Huang, Qianyu Zeng","doi":"10.4134/JKMS.J200086","DOIUrl":null,"url":null,"abstract":"For complete manifolds with α-Bach tensor (which is defined by (1.2)) flat, we provide some rigidity results characterized by some point-wise inequalities involving the Weyl curvature and the traceless Ricci curvature. Moveover, some Einstein metrics have also been characterized by some L n 2 -integral inequalities. Furthermore, we also give some rigidity characterizations for constant sectional curvature.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"41 1","pages":"401-418"},"PeriodicalIF":0.7000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"RIGIDITY CHARACTERIZATIONS OF COMPLETE RIEMANNIAN MANIFOLDS WITH α-BACH-FLAT\",\"authors\":\"Guangyue Huang, Qianyu Zeng\",\"doi\":\"10.4134/JKMS.J200086\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For complete manifolds with α-Bach tensor (which is defined by (1.2)) flat, we provide some rigidity results characterized by some point-wise inequalities involving the Weyl curvature and the traceless Ricci curvature. Moveover, some Einstein metrics have also been characterized by some L n 2 -integral inequalities. Furthermore, we also give some rigidity characterizations for constant sectional curvature.\",\"PeriodicalId\":49993,\"journal\":{\"name\":\"Journal of the Korean Mathematical Society\",\"volume\":\"41 1\",\"pages\":\"401-418\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Korean Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4134/JKMS.J200086\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Korean Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4134/JKMS.J200086","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: 0

摘要

对于α-Bach张量(由(1.2)定义)为平面的完全流形，我们给出了一些由涉及Weyl曲率和无迹Ricci曲率的点向不等式表征的刚性结果。此外，一些爱因斯坦度量也被一些l2积分不等式所表征。此外，我们还给出了等截面曲率下的一些刚性特性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

RIGIDITY CHARACTERIZATIONS OF COMPLETE RIEMANNIAN MANIFOLDS WITH α-BACH-FLAT

For complete manifolds with α-Bach tensor (which is defined by (1.2)) flat, we provide some rigidity results characterized by some point-wise inequalities involving the Weyl curvature and the traceless Ricci curvature. Moveover, some Einstein metrics have also been characterized by some L n 2 -integral inequalities. Furthermore, we also give some rigidity characterizations for constant sectional 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

Journal of the Korean Mathematical Society 数学-数学

CiteScore

1.20

自引率

16.70%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal endeavors to publish significant research of broad interests in pure and applied mathematics. One volume is published each year, and each volume consists of six issues (January, March, May, July, September, November).