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Riemannian manifolds with harmonic curvature

Volume 145 / 2016

Guangyue Huang, Bingqing Ma Colloquium Mathematicum 145 (2016), 251-257 MSC: Primary 53C20; Secondary 53C21. DOI: 10.4064/cm6826-4-2016 Published online: 4 July 2016

Abstract

We prove an integral inequality for compact $n$-dimensional manifolds with harmonic curvature tensor and positive scalar curvature, generalizing a recent result of Catino that deals with the conformally flat case, and classify those manifolds for which our inequality is an equality: they are either Einstein, $\mathbb {S}^1\times \mathbb {S}^{n-1}$ with the product metric, or $\mathbb {S}^1\times \mathbb {S}^{n-1}$ with a rotationally symmetric Derdziński metric.

Authors

  • Guangyue HuangCollege of Mathematics and Information Science
    Henan Normal University
    453007 Xinxiang, P.R. China
    and
    Henan Engineering Laboratory
    for Big Data Statistical Analysis
    and Optimal Control
    e-mail
  • Bingqing MaCollege of Mathematics and
    Information Science
    Henan Normal University
    453007 Xinxiang, P.R. China
    e-mail

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