New Characterizations of the Clifford Torus and the Calabi Torus.
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| Title: | New Characterizations of the Clifford Torus and the Calabi Torus. |
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| Authors: | Dehe Li1 lidehehe@163.com, Shujie Zhai2 zhaishujie@zzu.edu.cn |
| Source: | IAENG International Journal of Applied Mathematics. Aug2025, Vol. 55 Issue 8, p2373-2378. 6p. |
| Subjects: | Geometric rigidity, Curvature, Submanifolds, Calabi-Yau manifolds, Clifford algebras |
| Abstract: | Let Mn be a compact submanifold minimally immersed into the unit sphere Sn+p with codimension p, and denote by h the second fundamental form. As our main results, we first establish two rigidity theorems in terms of the geometric quantity σ(u) = ||h(u, u)||² for any unit vector u tangent to Mn, where || · ||² denotes the squared norm with respect to the standard metric g on Sn+p. Furthermore, we establish an optimal inequality for the conformally flat minimal Legendrian submanifolds in S2n+1 with constant scalar curvature, involving the normalized scalar curvature and the squared norms of the traceless Ricci tensor and second fundamental form. In particular, our first theorem related to the hypersurfaces of Sn+1 gives a new characterization of the Clifford torus, whereas the other theorems are about the Legendrian submanifolds such that new characterizations of the Calabi torus can be presented. [ABSTRACT FROM AUTHOR] |
| Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 187082278 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: New Characterizations of the Clifford Torus and the Calabi Torus. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Dehe+Li%22">Dehe Li</searchLink><relatesTo>1</relatesTo><i> lidehehe@163.com</i><br /><searchLink fieldCode="AR" term="%22Shujie+Zhai%22">Shujie Zhai</searchLink><relatesTo>2</relatesTo><i> zhaishujie@zzu.edu.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22IAENG+International+Journal+of+Applied+Mathematics%22">IAENG International Journal of Applied Mathematics</searchLink>. Aug2025, Vol. 55 Issue 8, p2373-2378. 6p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Geometric+rigidity%22">Geometric rigidity</searchLink><br /><searchLink fieldCode="DE" term="%22Curvature%22">Curvature</searchLink><br /><searchLink fieldCode="DE" term="%22Submanifolds%22">Submanifolds</searchLink><br /><searchLink fieldCode="DE" term="%22Calabi-Yau+manifolds%22">Calabi-Yau manifolds</searchLink><br /><searchLink fieldCode="DE" term="%22Clifford+algebras%22">Clifford algebras</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Let Mn be a compact submanifold minimally immersed into the unit sphere Sn+p with codimension p, and denote by h the second fundamental form. As our main results, we first establish two rigidity theorems in terms of the geometric quantity σ(u) = ||h(u, u)||² for any unit vector u tangent to Mn, where || · ||² denotes the squared norm with respect to the standard metric g on Sn+p. Furthermore, we establish an optimal inequality for the conformally flat minimal Legendrian submanifolds in S2n+1 with constant scalar curvature, involving the normalized scalar curvature and the squared norms of the traceless Ricci tensor and second fundamental form. In particular, our first theorem related to the hypersurfaces of Sn+1 gives a new characterization of the Clifford torus, whereas the other theorems are about the Legendrian submanifolds such that new characterizations of the Calabi torus can be presented. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 6 StartPage: 2373 Subjects: – SubjectFull: Geometric rigidity Type: general – SubjectFull: Curvature Type: general – SubjectFull: Submanifolds Type: general – SubjectFull: Calabi-Yau manifolds Type: general – SubjectFull: Clifford algebras Type: general Titles: – TitleFull: New Characterizations of the Clifford Torus and the Calabi Torus. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Dehe Li – PersonEntity: Name: NameFull: Shujie Zhai IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 08 Text: Aug2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 19929978 Numbering: – Type: volume Value: 55 – Type: issue Value: 8 Titles: – TitleFull: IAENG International Journal of Applied Mathematics Type: main |
| ResultId | 1 |
