具有正Yamabe不变量的爱因斯坦流形的刚性

IF 0.6 3区数学 Q3 MATHEMATICS

Annals of Global Analysis and Geometry Pub Date : 2025-05-21 DOI:10.1007/s10455-025-09996-x

L. Branca, G. Catino, D. Dameno, P. Mastrolia

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引用次数: 0

摘要

我们给出了任意维上具有正Yamabe不变量的闭爱因斯坦流形的最优捏合结果，扩展了四维上由于Gursky和LeBrun引起的标量曲率的最优界。我们还通过低维爱因斯坦流形的Weyl张量的\(L^{\frac{n}{2}}\) -范数改进了Yamabe不变量的已知界。最后，我们讨论了涉及维5和维6的Weyl张量的代数不等式的一些进展。

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Rigidity of Einstein manifolds with positive Yamabe invariant

We provide optimal pinching results on closed Einstein manifolds with positive Yamabe invariant in any dimension, extending the optimal bound for the scalar curvature due to Gursky and LeBrun in dimension four. We also improve the known bounds of the Yamabe invariant via the \(L^{\frac{n}{2}}\)-norm of the Weyl tensor for low-dimensional Einstein manifolds. Finally, we discuss some advances on an algebraic inequality involving the Weyl tensor for dimensions 5 and 6.

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来源期刊

Annals of Global Analysis and Geometry 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal examines global problems of geometry and analysis as well as the interactions between these fields and their application to problems of theoretical physics. It contributes to an enlargement of the international exchange of research results in the field. The areas covered in Annals of Global Analysis and Geometry include: global analysis, differential geometry, complex manifolds and related results from complex analysis and algebraic geometry, Lie groups, Lie transformation groups and harmonic analysis, variational calculus, applications of differential geometry and global analysis to problems of theoretical physics.