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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.10205 |
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| _version_ | 1866911394356527104 |
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| author | Wen, Yang |
| author_facet | Wen, Yang |
| contents | In this paper, we study the critical points of $F$-Yang-Mills functional on $\mathbb{C}P^n$, which are called $F$-Yang-Mills connections, which is a generalization of Yang-Mills connections. We prove that if $(2+\frac4n)F''(x)x+(n+1)F'(x)<0$, then the weakly stable $F$-Yang-Mills connection on $\mathbb{C}P^n$ must be flat. Moreover, if $(2+\frac4n)F''(x)x+(n+1)F'(x)=0$, we obtain the structure of curvatures corresponding to weakly stable connections. We also show a gap theorem for $F$-Yang-Mills connections on $\mathbb{C}P^n$. Our approach is inspired by Lawson-Simons' study of Yang-Mills stability on spheres. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10205 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The stability for F-Yang-Mills functional on CP^n Wen, Yang Differential Geometry In this paper, we study the critical points of $F$-Yang-Mills functional on $\mathbb{C}P^n$, which are called $F$-Yang-Mills connections, which is a generalization of Yang-Mills connections. We prove that if $(2+\frac4n)F''(x)x+(n+1)F'(x)<0$, then the weakly stable $F$-Yang-Mills connection on $\mathbb{C}P^n$ must be flat. Moreover, if $(2+\frac4n)F''(x)x+(n+1)F'(x)=0$, we obtain the structure of curvatures corresponding to weakly stable connections. We also show a gap theorem for $F$-Yang-Mills connections on $\mathbb{C}P^n$. Our approach is inspired by Lawson-Simons' study of Yang-Mills stability on spheres. |
| title | The stability for F-Yang-Mills functional on CP^n |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2501.10205 |