The stability of Fubini-Study metric on ℂℙⁿ

Guo, Xi; Li, Haizhong

doi:10.1090/proc/13594

The stability of Fubini-Study metric on $\mathbb {CP}^n$
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Proc. Amer. Math. Soc. 146 (2018), 325-333 Request permission

Abstract:

In this note, we study the stability of a critical point of a conformally invariant functional $\mathcal {F}$. For $n\geq 3$, by use of the variational formulas, we prove that the Fubini-Study metric on $\mathbb {CP}^n$ is a strictly stable critical point of $\mathcal {F}$.

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