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...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2024-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/2692876 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 2314-4785 |