Existence and Stability of α−Harmonic Maps
In this paper, we first study the α−energy functional, Euler-Lagrange operator, and α-stress-energy tensor. Second, it is shown that the critical points of the α−energy functional are explicitly related to harmonic maps through conformal deformation. In addition, an α−harmonic map is constructed fro...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2022-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/1906905 |
| _version_ | 1797985622358491136 |
|---|---|
| author | Seyed Mehdi Kazemi Torbaghan Keyvan Salehi Salman Babayi |
| author_facet | Seyed Mehdi Kazemi Torbaghan Keyvan Salehi Salman Babayi |
| author_sort | Seyed Mehdi Kazemi Torbaghan |
| collection | DOAJ |
| description | In this paper, we first study the α−energy functional, Euler-Lagrange operator, and α-stress-energy tensor. Second, it is shown that the critical points of the α−energy functional are explicitly related to harmonic maps through conformal deformation. In addition, an α−harmonic map is constructed from any smooth map between Riemannian manifolds under certain assumptions. Next, we determine the conditions under which the fibers of horizontally conformal α−harmonic maps are minimal submanifolds. Then, the stability of any α−harmonic map on Riemannian manifold with nonpositive curvature is studied. Finally, the instability of α−harmonic maps from a compact manifold to a standard unit sphere is investigated. |
| first_indexed | 2024-04-11T07:20:51Z |
| format | Article |
| id | doaj.art-6060e6e5a1744bf09e8b99ce2d9319fd |
| institution | Directory Open Access Journal |
| issn | 2314-4785 |
| language | English |
| last_indexed | 2024-04-11T07:20:51Z |
| publishDate | 2022-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj.art-6060e6e5a1744bf09e8b99ce2d9319fd2022-12-22T04:37:39ZengHindawi LimitedJournal of Mathematics2314-47852022-01-01202210.1155/2022/1906905Existence and Stability of α−Harmonic MapsSeyed Mehdi Kazemi Torbaghan0Keyvan Salehi1Salman Babayi2Department of MathematicsCentre of Theoretical Chemistry and Physics (CTCP)Department of MathematicsIn this paper, we first study the α−energy functional, Euler-Lagrange operator, and α-stress-energy tensor. Second, it is shown that the critical points of the α−energy functional are explicitly related to harmonic maps through conformal deformation. In addition, an α−harmonic map is constructed from any smooth map between Riemannian manifolds under certain assumptions. Next, we determine the conditions under which the fibers of horizontally conformal α−harmonic maps are minimal submanifolds. Then, the stability of any α−harmonic map on Riemannian manifold with nonpositive curvature is studied. Finally, the instability of α−harmonic maps from a compact manifold to a standard unit sphere is investigated.http://dx.doi.org/10.1155/2022/1906905 |
| spellingShingle | Seyed Mehdi Kazemi Torbaghan Keyvan Salehi Salman Babayi Existence and Stability of α−Harmonic Maps Journal of Mathematics |
| title | Existence and Stability of α−Harmonic Maps |
| title_full | Existence and Stability of α−Harmonic Maps |
| title_fullStr | Existence and Stability of α−Harmonic Maps |
| title_full_unstemmed | Existence and Stability of α−Harmonic Maps |
| title_short | Existence and Stability of α−Harmonic Maps |
| title_sort | existence and stability of α harmonic maps |
| url | http://dx.doi.org/10.1155/2022/1906905 |
| work_keys_str_mv | AT seyedmehdikazemitorbaghan existenceandstabilityofaharmonicmaps AT keyvansalehi existenceandstabilityofaharmonicmaps AT salmanbabayi existenceandstabilityofaharmonicmaps |