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

Guo, Xi; Li, Haizhong

doi:10.1090/proc/13594

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“…Stability of S p × S q and CP n for W n 2 has been studied in [9], [7], [6]. We prove the following result.…”

Section: Introductionmentioning

confidence: 84%

Stability of Quadratic curvature Functionals at product Einstein manifolds

Bhattacharya¹,

Maity²

2018

Preprint

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Consider Riemannian functionals defined by L 2 -norms of Ricci curvature, scalar curvature, Weyl curvature and Riemannian curvature. Rigidity, stability and local minimizing properties of Eistein metrics as critical metrics of these quadratic functionals have been studied in [8]. In this paper, we study the same for products of Einstein metrics with Einstein constants of possibly opposite signs. In particular, we prove that the product of a spherical space form and a compact hyperbolic manifold is unstable for certain quadratic functionals if the first eigenvalue of the Laplacian of the hyperbolic manifold is sufficiently small. We also prove the stability of L n 2 -norm of Weyl curvature at compact quotients of S n × H m .

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“…Stability of S p × S q and CP n for W n 2 has been studied in [9], [7], [6]. We prove the following result.…”

Section: Introductionmentioning

confidence: 84%