Hypersurfaces with Two Distinct Para-Blaschke Eigenvalues in Sn+1(1)
Let x:M↦Sn+1(1) be an n (n≥3)-dimensional immersed hypersurface without umbilical points and with vanishing Möbius form in a unit sphere Sn+1(1), and let A and B be the Blaschke tensor and the Möbius second fundamental form of x, respectively. We define a symmetric (0,2) tensor D=A+λB which is call...
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Wiley
2014-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2014/398746 |
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| author | Junfeng Chen Shichang Shu |
| author_facet | Junfeng Chen Shichang Shu |
| author_sort | Junfeng Chen |
| collection | DOAJ |
| description | Let x:M↦Sn+1(1) be an n (n≥3)-dimensional immersed hypersurface without umbilical points and with vanishing Möbius form in a unit sphere Sn+1(1), and let A and B be the Blaschke tensor and the Möbius second fundamental form of x, respectively. We define a symmetric (0,2) tensor D=A+λB which is called the para-Blaschke tensor of x, where λ is a constant. An eigenvalue of the para-Blaschke tensor is called a para-Blaschke eigenvalue of x. The aim of this paper is to classify the oriented hypersurfaces in Sn+1(1) with two distinct para-Blaschke eigenvalues under some rigidity conditions. |
| format | Article |
| id | doaj-art-8bc75c35886844da8fb1fe27509599aa |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
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| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-8bc75c35886844da8fb1fe27509599aa2025-02-03T05:59:26ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252014-01-01201410.1155/2014/398746398746Hypersurfaces with Two Distinct Para-Blaschke Eigenvalues in Sn+1(1)Junfeng Chen0Shichang Shu1School of Mathematics and Information Science, Xianyang Normal University, Xianyang, Shaanxi 712000, ChinaSchool of Mathematics and Information Science, Xianyang Normal University, Xianyang, Shaanxi 712000, ChinaLet x:M↦Sn+1(1) be an n (n≥3)-dimensional immersed hypersurface without umbilical points and with vanishing Möbius form in a unit sphere Sn+1(1), and let A and B be the Blaschke tensor and the Möbius second fundamental form of x, respectively. We define a symmetric (0,2) tensor D=A+λB which is called the para-Blaschke tensor of x, where λ is a constant. An eigenvalue of the para-Blaschke tensor is called a para-Blaschke eigenvalue of x. The aim of this paper is to classify the oriented hypersurfaces in Sn+1(1) with two distinct para-Blaschke eigenvalues under some rigidity conditions.http://dx.doi.org/10.1155/2014/398746 |
| spellingShingle | Junfeng Chen Shichang Shu Hypersurfaces with Two Distinct Para-Blaschke Eigenvalues in Sn+1(1) International Journal of Mathematics and Mathematical Sciences |
| title | Hypersurfaces with Two Distinct Para-Blaschke Eigenvalues in Sn+1(1) |
| title_full | Hypersurfaces with Two Distinct Para-Blaschke Eigenvalues in Sn+1(1) |
| title_fullStr | Hypersurfaces with Two Distinct Para-Blaschke Eigenvalues in Sn+1(1) |
| title_full_unstemmed | Hypersurfaces with Two Distinct Para-Blaschke Eigenvalues in Sn+1(1) |
| title_short | Hypersurfaces with Two Distinct Para-Blaschke Eigenvalues in Sn+1(1) |
| title_sort | hypersurfaces with two distinct para blaschke eigenvalues in sn 1 1 |
| url | http://dx.doi.org/10.1155/2014/398746 |
| work_keys_str_mv | AT junfengchen hypersurfaceswithtwodistinctparablaschkeeigenvaluesinsn11 AT shichangshu hypersurfaceswithtwodistinctparablaschkeeigenvaluesinsn11 |