### Abstract

We define a symmetric 2-tensor, called the J-tensor, canonically associated to the Q-curvature on any Riemannian manifold with dimension at least three. The relation between the J-tensor and the Q-curvature is like that between the Ricci tensor and the scalar curvature. Thus the J-tensor can be interpreted as a higher-order analogue of the Ricci tensor. This tensor can be used to understand the Chang-Gursky-Yang theorem on 4-dimensional Q-singular metrics. We show that an almost-Schur lemma holds for the Qcurvature, yielding an estimate of the Q-curvature on closed manifolds.

Original language | English (US) |
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Pages (from-to) | 425-438 |

Number of pages | 14 |

Journal | Pacific Journal of Mathematics |

Volume | 291 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 2017 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Keywords

- J-tensor
- Q-curvature
- Q-singular metric

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## Cite this

Lin, Y. J., & Yuan, W. (2017). A Symmetric 2-Tensor canonically associated to Q-curvature and its applications.

*Pacific Journal of Mathematics*,*291*(2), 425-438. https://doi.org/10.2140/pjm.2017.291.425