Rigidity of complete manifolds with parallel Cotton tensor
The aim of this paper is to show some rigidity results for complete Riemannian manifolds with parallel Cotton tensor. In particular, we prove that any compact manifold of dimension n ≥ 3 with parallel Cotton tensor and positive constant scalar curvature is isometric to a finite quotient of S n under...
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| Veröffentlicht in: | Archiv der Mathematik 2017-08, Vol.109 (2), p.179-189 |
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| creator | Chu, Yawei Fang, Shouwen |
| description | The aim of this paper is to show some rigidity results for complete Riemannian manifolds with parallel Cotton tensor. In particular, we prove that any compact manifold of dimension
n
≥
3
with parallel Cotton tensor and positive constant scalar curvature is isometric to a finite quotient of
S
n
under a pointwise or integral pinching condition. Moreover, a rigidity theorem for stochastically complete manifolds with parallel Cotton tensor is also given. The proofs rely mainly on curvature elliptic estimates and the weak maximum principle. |
| doi_str_mv | 10.1007/s00013-017-1047-y |
| format | Article |
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n
≥
3
with parallel Cotton tensor and positive constant scalar curvature is isometric to a finite quotient of
S
n
under a pointwise or integral pinching condition. Moreover, a rigidity theorem for stochastically complete manifolds with parallel Cotton tensor is also given. The proofs rely mainly on curvature elliptic estimates and the weak maximum principle.</description><identifier>ISSN: 0003-889X</identifier><identifier>EISSN: 1420-8938</identifier><identifier>DOI: 10.1007/s00013-017-1047-y</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Cotton ; Curvature ; Manifolds (mathematics) ; Mathematics ; Mathematics and Statistics ; Maximum principle ; Probability theory ; Randomness ; Rigidity</subject><ispartof>Archiv der Mathematik, 2017-08, Vol.109 (2), p.179-189</ispartof><rights>Springer International Publishing 2017</rights><rights>Copyright Springer Science & Business Media 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-24e15fdad4846688951fb48ffb08dd58f35ef0fb1552f4d3c45183386c974b5c3</citedby><cites>FETCH-LOGICAL-c316t-24e15fdad4846688951fb48ffb08dd58f35ef0fb1552f4d3c45183386c974b5c3</cites><orcidid>0000-0002-6818-3048</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00013-017-1047-y$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00013-017-1047-y$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Chu, Yawei</creatorcontrib><creatorcontrib>Fang, Shouwen</creatorcontrib><title>Rigidity of complete manifolds with parallel Cotton tensor</title><title>Archiv der Mathematik</title><addtitle>Arch. Math</addtitle><description>The aim of this paper is to show some rigidity results for complete Riemannian manifolds with parallel Cotton tensor. In particular, we prove that any compact manifold of dimension
n
≥
3
with parallel Cotton tensor and positive constant scalar curvature is isometric to a finite quotient of
S
n
under a pointwise or integral pinching condition. Moreover, a rigidity theorem for stochastically complete manifolds with parallel Cotton tensor is also given. The proofs rely mainly on curvature elliptic estimates and the weak maximum principle.</description><subject>Cotton</subject><subject>Curvature</subject><subject>Manifolds (mathematics)</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Maximum principle</subject><subject>Probability theory</subject><subject>Randomness</subject><subject>Rigidity</subject><issn>0003-889X</issn><issn>1420-8938</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp1kE1LxDAQhoMouK7-AG8Bz9FMPtrUmyx-wYIgCt5C2yRrl25TkyzSf2-WevDiaQ7zPu8MD0KXQK-B0vImUkqBEwolASpKMh2hBQhGiaq4OkaLvOZEqerjFJ3FuM1hpspqgW5fu01nujRh73Drd2Nvk8W7euic703E3136xGMd6r63PV75lPyAkx2iD-foxNV9tBe_c4neH-7fVk9k_fL4vLpbk5ZDkQgTFqQztRFKFEV-QYJrhHKuocoYqRyX1lHXgJTMCcNbIUFxroq2KkUjW75EV3PvGPzX3sakt34fhnxSQ8UorwqWgSWCOdUGH2OwTo-h29Vh0kD1QZGeFemsSB8U6SkzbGZizg4bG_40_wv9AIfeaSc</recordid><startdate>20170801</startdate><enddate>20170801</enddate><creator>Chu, Yawei</creator><creator>Fang, Shouwen</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-6818-3048</orcidid></search><sort><creationdate>20170801</creationdate><title>Rigidity of complete manifolds with parallel Cotton tensor</title><author>Chu, Yawei ; Fang, Shouwen</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-24e15fdad4846688951fb48ffb08dd58f35ef0fb1552f4d3c45183386c974b5c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Cotton</topic><topic>Curvature</topic><topic>Manifolds (mathematics)</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Maximum principle</topic><topic>Probability theory</topic><topic>Randomness</topic><topic>Rigidity</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chu, Yawei</creatorcontrib><creatorcontrib>Fang, Shouwen</creatorcontrib><collection>CrossRef</collection><jtitle>Archiv der Mathematik</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chu, Yawei</au><au>Fang, Shouwen</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Rigidity of complete manifolds with parallel Cotton tensor</atitle><jtitle>Archiv der Mathematik</jtitle><stitle>Arch. Math</stitle><date>2017-08-01</date><risdate>2017</risdate><volume>109</volume><issue>2</issue><spage>179</spage><epage>189</epage><pages>179-189</pages><issn>0003-889X</issn><eissn>1420-8938</eissn><abstract>The aim of this paper is to show some rigidity results for complete Riemannian manifolds with parallel Cotton tensor. In particular, we prove that any compact manifold of dimension
n
≥
3
with parallel Cotton tensor and positive constant scalar curvature is isometric to a finite quotient of
S
n
under a pointwise or integral pinching condition. Moreover, a rigidity theorem for stochastically complete manifolds with parallel Cotton tensor is also given. The proofs rely mainly on curvature elliptic estimates and the weak maximum principle.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00013-017-1047-y</doi><tpages>11</tpages><orcidid>https://orcid.org/0000-0002-6818-3048</orcidid></addata></record> |
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| ispartof | Archiv der Mathematik, 2017-08, Vol.109 (2), p.179-189 |
| issn | 0003-889X 1420-8938 |
| language | eng |
| recordid | cdi_proquest_journals_1920396218 |
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| subjects | Cotton Curvature Manifolds (mathematics) Mathematics Mathematics and Statistics Maximum principle Probability theory Randomness Rigidity |
| title | Rigidity of complete manifolds with parallel Cotton tensor |
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