{"title":"FIRST EIGENVALUE CHARACTERISATION OF CLIFFORD HYPERSURFACES AND VERONESE SURFACES","authors":"PEIYI WU","doi":"10.1017/s0004972724000273","DOIUrl":null,"url":null,"abstract":"\n\t <jats:p>We give a sharp estimate for the first eigenvalue of the Schrödinger operator <jats:inline-formula>\n\t <jats:alternatives>\n\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972724000273_inline1.png\"/>\n\t\t<jats:tex-math>\n$L:=-\\Delta -\\sigma $\n</jats:tex-math>\n\t </jats:alternatives>\n\t </jats:inline-formula> which is defined on the closed minimal submanifold <jats:inline-formula>\n\t <jats:alternatives>\n\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972724000273_inline2.png\"/>\n\t\t<jats:tex-math>\n$M^{n}$\n</jats:tex-math>\n\t </jats:alternatives>\n\t </jats:inline-formula> in the unit sphere <jats:inline-formula>\n\t <jats:alternatives>\n\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972724000273_inline3.png\"/>\n\t\t<jats:tex-math>\n$\\mathbb {S}^{n+m}$\n</jats:tex-math>\n\t </jats:alternatives>\n\t </jats:inline-formula>, where <jats:inline-formula>\n\t <jats:alternatives>\n\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972724000273_inline4.png\"/>\n\t\t<jats:tex-math>\n$\\sigma $\n</jats:tex-math>\n\t </jats:alternatives>\n\t </jats:inline-formula> is the square norm of the second fundamental form.</jats:p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s0004972724000273","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We give a sharp estimate for the first eigenvalue of the Schrödinger operator
$L:=-\Delta -\sigma $
which is defined on the closed minimal submanifold
$M^{n}$
in the unit sphere
$\mathbb {S}^{n+m}$
, where
$\sigma $
is the square norm of the second fundamental form.