A GJMS construction for 2-tensors and the second variation of the total<i>Q</i>-curvature

Abstract

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