The Morse Index of Sacks–Uhlenbeck α-Harmonic Maps for Riemannian Manifolds
In this paper, first we prove a nonexistence theorem for α-harmonic mappings between Riemannian manifolds. Second, the instability of nonconstant α-harmonic maps is studied with regard to the Ricci curvature criterion of their codomain. Then, we estimate the Morse index for measuring the degree of i...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/2692876 |
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| author | Amir Shahnavaz Nader Kouhestani Seyed Mehdi Kazemi Torbaghan |
| author_facet | Amir Shahnavaz Nader Kouhestani Seyed Mehdi Kazemi Torbaghan |
| author_sort | Amir Shahnavaz |
| collection | DOAJ |
| description | In this paper, first we prove a nonexistence theorem for α-harmonic mappings between Riemannian manifolds. Second, the instability of nonconstant α-harmonic maps is studied with regard to the Ricci curvature criterion of their codomain. Then, we estimate the Morse index for measuring the degree of instability of some particular α-harmonic maps. Furthermore, the notion of α-stable manifolds and its applications are considered. Finally, we investigate the α-stability of any compact Riemannian manifolds admitting a nonisometric conformal vector field and any Einstein Riemannian manifold under certain assumptions on the smallest positive eigenvalue of its Laplacian operator on functions. |
| format | Article |
| id | doaj-art-f8b7da58822642a691d56c6a5a24a8af |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-f8b7da58822642a691d56c6a5a24a8af2025-02-03T01:30:22ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/2024/2692876The Morse Index of Sacks–Uhlenbeck α-Harmonic Maps for Riemannian ManifoldsAmir Shahnavaz0Nader Kouhestani1Seyed Mehdi Kazemi Torbaghan2Department of MathematicsDepartment of MathematicsDepartment of MathematicsIn this paper, first we prove a nonexistence theorem for α-harmonic mappings between Riemannian manifolds. Second, the instability of nonconstant α-harmonic maps is studied with regard to the Ricci curvature criterion of their codomain. Then, we estimate the Morse index for measuring the degree of instability of some particular α-harmonic maps. Furthermore, the notion of α-stable manifolds and its applications are considered. Finally, we investigate the α-stability of any compact Riemannian manifolds admitting a nonisometric conformal vector field and any Einstein Riemannian manifold under certain assumptions on the smallest positive eigenvalue of its Laplacian operator on functions.http://dx.doi.org/10.1155/2024/2692876 |
| spellingShingle | Amir Shahnavaz Nader Kouhestani Seyed Mehdi Kazemi Torbaghan The Morse Index of Sacks–Uhlenbeck α-Harmonic Maps for Riemannian Manifolds Journal of Mathematics |
| title | The Morse Index of Sacks–Uhlenbeck α-Harmonic Maps for Riemannian Manifolds |
| title_full | The Morse Index of Sacks–Uhlenbeck α-Harmonic Maps for Riemannian Manifolds |
| title_fullStr | The Morse Index of Sacks–Uhlenbeck α-Harmonic Maps for Riemannian Manifolds |
| title_full_unstemmed | The Morse Index of Sacks–Uhlenbeck α-Harmonic Maps for Riemannian Manifolds |
| title_short | The Morse Index of Sacks–Uhlenbeck α-Harmonic Maps for Riemannian Manifolds |
| title_sort | morse index of sacks uhlenbeck α harmonic maps for riemannian manifolds |
| url | http://dx.doi.org/10.1155/2024/2692876 |
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