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 - 2017 |
All Science Journal Classification (ASJC) codes
- General Mathematics
Keywords
- J-tensor
- Q-curvature
- Q-singular metric