具有α-bach-flat的完全黎曼流形的刚性表征

Pub Date : 2021-01-01 DOI:10.4134/JKMS.J200086

Guangyue Huang, Qianyu Zeng

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引用次数: 0

摘要

对于α-Bach张量(由(1.2)定义)为平面的完全流形，我们给出了一些由涉及Weyl曲率和无迹Ricci曲率的点向不等式表征的刚性结果。此外，一些爱因斯坦度量也被一些l2积分不等式所表征。此外，我们还给出了等截面曲率下的一些刚性特性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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RIGIDITY CHARACTERIZATIONS OF COMPLETE RIEMANNIAN MANIFOLDS WITH α-BACH-FLAT

For complete manifolds with α-Bach tensor (which is defined by (1.2)) flat, we provide some rigidity results characterized by some point-wise inequalities involving the Weyl curvature and the traceless Ricci curvature. Moveover, some Einstein metrics have also been characterized by some L n 2 -integral inequalities. Furthermore, we also give some rigidity characterizations for constant sectional curvature.

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