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

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

2012-02-15

arxiv.org/abs/1202.3227v1

Mathematics

Differential Geometry

15 pages

Scientific paper

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.

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