The Ambient Obstruction Tensor and Q-Curvature

TL;DR

This paper establishes a fundamental link between the variational derivative of Q-curvature and the ambient obstruction tensor, providing new insights into conformal invariants and their classifications.

Contribution

It demonstrates that the variational derivative of the integral of Q-curvature equals the ambient obstruction tensor, and classifies conformally invariant tensors modulo higher order curvature terms.

Findings

The variational derivative of Q-curvature integral equals the ambient obstruction tensor.

A classification of irreducible conformally invariant tensors is provided.

The work clarifies the structure of conformal invariants in differential geometry.

Abstract

It is shown that the variational derivative of the integral of Branson's Q-curvature is the ambient obstruction tensor of Fefferman-Graham. A classification of irreducible conformally invariant tensors modulo quadratic and higher degree terms in curvature is established.