{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T15:39:01Z","timestamp":1746805141329,"version":"3.40.5"},"reference-count":12,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"Shaanxi Education Department","award":["11JK0479"],"award-info":[{"award-number":["11JK0479"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>Let<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mi mathvariant=\"bold\">x<\/mml:mi><mml:mo>:<\/mml:mo><mml:mi>M<\/mml:mi><mml:mo>\u21a6<\/mml:mo><mml:msup><mml:mrow><mml:mi>S<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>n<\/mml:mi><mml:mo>+<\/mml:mo><mml:mn mathvariant=\"normal\">1<\/mml:mn><\/mml:mrow><\/mml:msup><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mn mathvariant=\"normal\">1<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>be an<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mi>n\u2009\u2009<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>n<\/mml:mi><mml:mo>\u2265<\/mml:mo><mml:mn mathvariant=\"normal\">3<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>-dimensional immersed hypersurface without umbilical points and with vanishing M\u00f6bius form in a unit sphere<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:msup><mml:mrow><mml:mi>S<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>n<\/mml:mi><mml:mo>+<\/mml:mo><mml:mn mathvariant=\"normal\">1<\/mml:mn><\/mml:mrow><\/mml:msup><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mn mathvariant=\"normal\">1<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>, and let<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:mi mathvariant=\"bold\">A<\/mml:mi><\/mml:mrow><\/mml:math>and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mrow><mml:mi mathvariant=\"bold\">B<\/mml:mi><\/mml:mrow><\/mml:math>be the Blaschke tensor and the M\u00f6bius second fundamental form of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><mml:mrow><mml:mi mathvariant=\"bold\">x<\/mml:mi><\/mml:mrow><\/mml:math>, respectively. We define a symmetric<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M8\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mn mathvariant=\"normal\">0,2<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>tensor<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M9\"><mml:mi mathvariant=\"bold\">D<\/mml:mi><mml:mo>=<\/mml:mo><mml:mi mathvariant=\"bold\">A<\/mml:mi><mml:mo>+<\/mml:mo><mml:mi>\u03bb<\/mml:mi><mml:mi mathvariant=\"bold\">B<\/mml:mi><\/mml:math>which is called the para-Blaschke tensor of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M10\"><mml:mrow><mml:mi mathvariant=\"bold\">x<\/mml:mi><\/mml:mrow><\/mml:math>, where<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M11\"><mml:mrow><mml:mi>\u03bb<\/mml:mi><\/mml:mrow><\/mml:math>is a constant. An eigenvalue of the para-Blaschke tensor is called<jats:italic>a para-Blaschke eigenvalue<\/jats:italic>of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M12\"><mml:mrow><mml:mi mathvariant=\"bold\">x<\/mml:mi><\/mml:mrow><\/mml:math>. The aim of this paper is to classify the oriented hypersurfaces in<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M13\"><mml:msup><mml:mrow><mml:mi>S<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>n<\/mml:mi><mml:mo>+<\/mml:mo><mml:mn mathvariant=\"normal\">1<\/mml:mn><\/mml:mrow><\/mml:msup><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mn mathvariant=\"normal\">1<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>with two distinct para-Blaschke eigenvalues under some rigidity conditions.<\/jats:p>","DOI":"10.1155\/2014\/398746","type":"journal-article","created":{"date-parts":[[2014,4,14]],"date-time":"2014-04-14T17:03:19Z","timestamp":1397494999000},"page":"1-10","source":"Crossref","is-referenced-by-count":0,"title":["Hypersurfaces with Two Distinct Para-Blaschke Eigenvalues in<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:msup><mml:mrow><mml:mi>S<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>n<\/mml:mi><mml:mo>+<\/mml:mo><mml:mn fontstyle=\"italic\">1<\/mml:mn><\/mml:mrow><\/mml:msup><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mn fontstyle=\"italic\">1<\/mml:mn><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>"],"prefix":"10.1155","volume":"2014","author":[{"given":"Junfeng","family":"Chen","sequence":"first","affiliation":[{"name":"School of Mathematics and Information Science, Xianyang Normal University, Xianyang, Shaanxi 712000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shichang","family":"Shu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Information Science, Xianyang Normal University, Xianyang, Shaanxi 712000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"11","doi-asserted-by":"publisher","DOI":"10.1007\/s002290050080"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1002\/9781118032633"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-97-03828-8"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.2969\/jmsj\/1156342043"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1360\/03ys0134"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1007\/s10114-002-0173-y"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1007\/s00229-003-0383-3"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1007\/s10114-005-0919-4"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.2748\/tmj\/1113247800"},{"issue":"3","key":"12","first-page":"579","volume":"51","year":"2008","journal-title":"Acta Mathematica Sinica. 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