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arXiv · 1602.01212

A symmetric 2-tensor canonically associated to Q-curvature and its applications

Yueh-Ju Lin·Wei Yuan
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Abstract

In this article, we define a symmetric 2-tensor canonically associated to Q-curvature called J-tensor on any Riemannian manifold with dimension at least three. The relation between J-tensor and Q-curvature is precisely like Ricci tensor and scalar curvature. Thus it can be interpreted as a higher-order analogue of Ricci tensor. This tensor can also be used to understand Chang-Gursky-Yang's theorem on 4-dimensional Q-singular metrics. Moreover, we show an Almost-Schur Lemma holds for Q-curvature, which gives an estimate of Q-curvature on closed manifolds.

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Yueh-Ju Lin, Wei Yuan. 2016-02-03. A symmetric 2-tensor canonically associated to Q-curvature and its applications. https://doi.org/10.2140/pjm.2017.291.425

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