A GJMS construction for 2-tensors and the second variation of the total Q-curvature

Abstract

We construct a series of conformally invariant differential operators acting on weighted trace-free symmetric 2-tensors by a method similar to Graham-Jenne-Mason-Sparling's. For compact conformal manifolds of dimension even and greater than or equal to four with vanishing ambient obstruction tensor, one of these operators is used to describe the second variation of the total Q-curvature. An explicit formula for conformally Einstein manifolds is given in terms of the Lichnerowicz Laplacian of an Einstein representative metric.

16 pages; Introduction revised, minor changes elsewhere

References in corpus (2)

• The Ambient Obstruction Tensor and Q-Curvature
• Rigidity of conformal functionals on spheres

Cited by in corpus (6)

• Ambient constructions for Sasakian $\eta$-Einstein manifolds
• Deformations of Q-curvature II
• GJMS-like operators on symmetric 2-tensors and their gravitational duals
• On the second variation of the Graham-Witten energy
• Q-curvature of Weyl structures and Poincaré metrics
• One-loop divergences in 7D Einstein and 6D Conformal Gravities