Weakly stable irreducible Yang-Mills fields over $S^4$
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914405239750656 |
|---|---|
| author | Ge, Jianquan Xiao, Lixin |
| author_facet | Ge, Jianquan Xiao, Lixin |
| contents | Addressing Yau's conjecture (Problem 117) on $S^4$, we investigate the self-duality of weakly stable Yang-Mills fields under the assumption of irreducibility. For structure groups with a simple Lie algebra, we prove that any weakly stable irreducible connection must be either self-dual or anti-self-dual. Furthermore, we demonstrate that if the Lie algebra admits a non-trivial abelian center, no irreducible Yang-Mills fields can exist over $S^4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_17352 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weakly stable irreducible Yang-Mills fields over $S^4$ Ge, Jianquan Xiao, Lixin Differential Geometry 58E15, 53C07 Addressing Yau's conjecture (Problem 117) on $S^4$, we investigate the self-duality of weakly stable Yang-Mills fields under the assumption of irreducibility. For structure groups with a simple Lie algebra, we prove that any weakly stable irreducible connection must be either self-dual or anti-self-dual. Furthermore, we demonstrate that if the Lie algebra admits a non-trivial abelian center, no irreducible Yang-Mills fields can exist over $S^4$. |
| title | Weakly stable irreducible Yang-Mills fields over $S^4$ |
| topic | Differential Geometry 58E15, 53C07 |
| url | https://arxiv.org/abs/2603.17352 |