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The stability of Fubini-Study metric on $ \mathbb{CP}^n$


Authors: Xi Guo and Haizhong Li
Journal: Proc. Amer. Math. Soc. 146 (2018), 325-333
MSC (2010): Primary 53C20, 58E11
DOI: https://doi.org/10.1090/proc/13594
Published electronically: September 27, 2017
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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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Additional Information

Xi Guo
Affiliation: Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan 430062, People’s Republic of China
Email: guoxi@hubu.edu.cn

Haizhong Li
Affiliation: Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, People’s Republic of China
Email: hli@math.tsinghua.edu.cn

DOI: https://doi.org/10.1090/proc/13594
Keywords: Weyl curvature tensor, Riemannian functional, stability
Received by editor(s): June 18, 2016
Received by editor(s) in revised form: November 17, 2016
Published electronically: September 27, 2017
Additional Notes: The first author was supported by grant NSFC-11501184
The second author was supported by grant NSFC-11671224
Communicated by: Guofang Wei
Article copyright: © Copyright 2017 American Mathematical Society

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