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

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.

14 pages, new remarks, references and acknowledgement added in the introduction

References in corpus (1)

• A Quartic Conformally Covariant Differential Operator for Arbitrary Pseudo-Riemannian Manifolds (Summary)

Cited by in corpus (3)

• Nonuniqueness of conformal metrics with constant $Q$-curvature
• $Q$-curvature and gravity
• Compactness within the space of complete, constant Q-curvature metrics on the sphere with isolated singularities