Characterizing small spheres in a unit sphere by Fischer–Marsden equation
Abstract We use a nontrivial concircular vector field u on the unit sphere S n + 1 $\mathbf{S}^{n+1}$ in studying geometry of its hypersurfaces. An orientable hypersurface M of the unit sphere S n + 1 $\mathbf{S}^{n+1}$ naturally inherits a vector field v and a smooth function ρ. We use the conditio...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-09-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-022-02855-4 |
| _version_ | 1811273668347559936 |
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| author | Nasser Bin Turki Sharief Deshmukh Gabriel-Eduard Vîlcu |
| author_facet | Nasser Bin Turki Sharief Deshmukh Gabriel-Eduard Vîlcu |
| author_sort | Nasser Bin Turki |
| collection | DOAJ |
| description | Abstract We use a nontrivial concircular vector field u on the unit sphere S n + 1 $\mathbf{S}^{n+1}$ in studying geometry of its hypersurfaces. An orientable hypersurface M of the unit sphere S n + 1 $\mathbf{S}^{n+1}$ naturally inherits a vector field v and a smooth function ρ. We use the condition that the vector field v is an eigenvector of the de-Rham Laplace operator together with an inequality satisfied by the integral of the Ricci curvature in the direction of the vector field v to find a characterization of small spheres in the unit sphere S n + 1 $\mathbf{S}^{n+1}$ . We also use the condition that the function ρ is a nontrivial solution of the Fischer–Marsden equation together with an inequality satisfied by the integral of the Ricci curvature in the direction of the vector field v to find another characterization of small spheres in the unit sphere S n + 1 $\mathbf{S}^{n+1}$ . |
| first_indexed | 2024-04-12T23:03:23Z |
| format | Article |
| id | doaj.art-5c076729a49f4edca53cfa09522a8763 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-04-12T23:03:23Z |
| publishDate | 2022-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-5c076729a49f4edca53cfa09522a87632022-12-22T03:12:58ZengSpringerOpenJournal of Inequalities and Applications1029-242X2022-09-012022111310.1186/s13660-022-02855-4Characterizing small spheres in a unit sphere by Fischer–Marsden equationNasser Bin Turki0Sharief Deshmukh1Gabriel-Eduard Vîlcu2Department of Mathematics, College of Science, King Saud UniversityDepartment of Mathematics, College of Science, King Saud UniversityDepartment of Mathematics and Informatics, Faculty of Applied Sciences, Politehnica of BucharestAbstract We use a nontrivial concircular vector field u on the unit sphere S n + 1 $\mathbf{S}^{n+1}$ in studying geometry of its hypersurfaces. An orientable hypersurface M of the unit sphere S n + 1 $\mathbf{S}^{n+1}$ naturally inherits a vector field v and a smooth function ρ. We use the condition that the vector field v is an eigenvector of the de-Rham Laplace operator together with an inequality satisfied by the integral of the Ricci curvature in the direction of the vector field v to find a characterization of small spheres in the unit sphere S n + 1 $\mathbf{S}^{n+1}$ . We also use the condition that the function ρ is a nontrivial solution of the Fischer–Marsden equation together with an inequality satisfied by the integral of the Ricci curvature in the direction of the vector field v to find another characterization of small spheres in the unit sphere S n + 1 $\mathbf{S}^{n+1}$ .https://doi.org/10.1186/s13660-022-02855-4Spherede-Rham Laplace operatorFischer–Marsden differential equationSmall sphere |
| spellingShingle | Nasser Bin Turki Sharief Deshmukh Gabriel-Eduard Vîlcu Characterizing small spheres in a unit sphere by Fischer–Marsden equation Journal of Inequalities and Applications Sphere de-Rham Laplace operator Fischer–Marsden differential equation Small sphere |
| title | Characterizing small spheres in a unit sphere by Fischer–Marsden equation |
| title_full | Characterizing small spheres in a unit sphere by Fischer–Marsden equation |
| title_fullStr | Characterizing small spheres in a unit sphere by Fischer–Marsden equation |
| title_full_unstemmed | Characterizing small spheres in a unit sphere by Fischer–Marsden equation |
| title_short | Characterizing small spheres in a unit sphere by Fischer–Marsden equation |
| title_sort | characterizing small spheres in a unit sphere by fischer marsden equation |
| topic | Sphere de-Rham Laplace operator Fischer–Marsden differential equation Small sphere |
| url | https://doi.org/10.1186/s13660-022-02855-4 |
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