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arXiv · 2501.10205

The stability for F-Yang-Mills functional on CP^n

Yang Wen
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Abstract

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.

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Yang Wen. 2025-01-17. The stability for F-Yang-Mills functional on CP^n. https://arxiv.org/abs/2501.10205

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