闭黎曼流形上二次曲率函数临界度量的刚性

IF 0.4 4区数学 Q4 MATHEMATICS

Colloquium Mathematicum Pub Date : 2022-01-01 DOI:10.4064/cm8236-6-2021

B. Ma, Guangyue Huang

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引用次数: 0

摘要

．研究涉及标量曲率、里奇曲率和黎曼曲率张量的二次曲率函数F、s (g)的临界度量的刚性。特别地，当s = 0时，我们用涉及Weyl曲率和无迹Ricci张量的点向不等式给出了具有无散度Cotton张量的临界度量的新的表征。我们还提供了一些局部共形平面临界指标的刚性结果。二次53 c21。

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Rigidity of critical metrics for quadratic curvature functions on closed Riemannian manifolds

. We study rigidity of critical metrics for quadratic curvature functions F t,s ( g ) involving the scalar curvature, the Ricci curvature and the Riemannian curvature tensor. In particular, when s = 0 , we give new characterizations by pointwise inequali-ties involving the Weyl curvature and the traceless Ricci tensor for critical metrics with divergence-free Cotton tensor. We also provide a few rigidity results for locally conformally flat critical metrics. Secondary 53C21.

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来源期刊

Colloquium Mathematicum MATHEMATICS-

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Colloquium Mathematicum is a journal devoted to the publication of original papers of moderate length addressed to a broad mathematical audience. It publishes results of original research, interesting new proofs of important theorems and research-expository papers in all fields of pure mathematics. Two issues constitute a volume, and at least four volumes are published each year.