On 1-index of Unstable Spacelike Hypersurfaces in Pseudo-Euclidean Spheres
In mathematical physics, the stable hypersurfaces of constant mean curvature in pseudo-Euclidian spheres have been interested by many researchers on general relativity. As an extension, the notion of index of stability has been introduced for unstable ones. The stability index (as a rate of distance...
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| Format: | Article |
| Language: | English |
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University of Maragheh
2021-12-01
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| Series: | Sahand Communications in Mathematical Analysis |
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| Online Access: | https://scma.maragheh.ac.ir/article_248103_e470e8ed71d63e0d14235a8da8e7b331.pdf |
| _version_ | 1818018665934618624 |
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| author | Behzad Esmaeili Firooz Pashaie Ghorbanali Haghighatdoost |
| author_facet | Behzad Esmaeili Firooz Pashaie Ghorbanali Haghighatdoost |
| author_sort | Behzad Esmaeili |
| collection | DOAJ |
| description | In mathematical physics, the stable hypersurfaces of constant mean curvature in pseudo-Euclidian spheres have been interested by many researchers on general relativity. As an extension, the notion of index of stability has been introduced for unstable ones. The stability index (as a rate of distance from being stable) is defined in terms of the Laplace operator $\Delta$ as the trace of Hessian tensor. In this paper, we study an extension of stability index(namely, 1-index) of hypersurfaces with constant scalar curvature in pseudo-Euclidian sphere $\S_1^{n+1}$. 1-index is defined based on the Cheng-Yau operator $\Box$ as a natural extension of $\Delta$. |
| first_indexed | 2024-04-14T07:42:51Z |
| format | Article |
| id | doaj.art-f46da4cb9a33425e9c0912bbc4c7cd0e |
| institution | Directory Open Access Journal |
| issn | 2322-5807 2423-3900 |
| language | English |
| last_indexed | 2024-04-14T07:42:51Z |
| publishDate | 2021-12-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj.art-f46da4cb9a33425e9c0912bbc4c7cd0e2022-12-22T02:05:26ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002021-12-011849711110.22130/scma.2021.541680.1009248103On 1-index of Unstable Spacelike Hypersurfaces in Pseudo-Euclidean SpheresBehzad Esmaeili0Firooz Pashaie1Ghorbanali Haghighatdoost2Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.Department of Mathematics, Faculty of Sciences, University of Maragheh, P.O.Box 55181-83111, Maragheh, Iran.Department of Mathematics, Azarbaijan Shahid Madani University, P.O.Box 53714-161, Tabriz, Iran.In mathematical physics, the stable hypersurfaces of constant mean curvature in pseudo-Euclidian spheres have been interested by many researchers on general relativity. As an extension, the notion of index of stability has been introduced for unstable ones. The stability index (as a rate of distance from being stable) is defined in terms of the Laplace operator $\Delta$ as the trace of Hessian tensor. In this paper, we study an extension of stability index(namely, 1-index) of hypersurfaces with constant scalar curvature in pseudo-Euclidian sphere $\S_1^{n+1}$. 1-index is defined based on the Cheng-Yau operator $\Box$ as a natural extension of $\Delta$.https://scma.maragheh.ac.ir/article_248103_e470e8ed71d63e0d14235a8da8e7b331.pdfspacelikenewton transformationlorentz-minkowski space1-minimal hypersurface |
| spellingShingle | Behzad Esmaeili Firooz Pashaie Ghorbanali Haghighatdoost On 1-index of Unstable Spacelike Hypersurfaces in Pseudo-Euclidean Spheres Sahand Communications in Mathematical Analysis spacelike newton transformation lorentz-minkowski space 1-minimal hypersurface |
| title | On 1-index of Unstable Spacelike Hypersurfaces in Pseudo-Euclidean Spheres |
| title_full | On 1-index of Unstable Spacelike Hypersurfaces in Pseudo-Euclidean Spheres |
| title_fullStr | On 1-index of Unstable Spacelike Hypersurfaces in Pseudo-Euclidean Spheres |
| title_full_unstemmed | On 1-index of Unstable Spacelike Hypersurfaces in Pseudo-Euclidean Spheres |
| title_short | On 1-index of Unstable Spacelike Hypersurfaces in Pseudo-Euclidean Spheres |
| title_sort | on 1 index of unstable spacelike hypersurfaces in pseudo euclidean spheres |
| topic | spacelike newton transformation lorentz-minkowski space 1-minimal hypersurface |
| url | https://scma.maragheh.ac.ir/article_248103_e470e8ed71d63e0d14235a8da8e7b331.pdf |
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