TT-eigentensors for the Lichnerowicz Laplacian on some asymptotically hyperbolic manifolds with warped products metrics

Abstract

Let (M =]0, ∞[×N, g) be an asymptotically hyperbolic manifold of dimension n + 1 ≥ 3, equipped with a warped product metric. We show that there exist no TT L 2-eigentensors with eigenvalue in the essential spectrum of the Lichnerowicz Laplacian Δ L . If (M, g) is the real hyperbolic space, there is no symmetric L 2-eigentensors of Δ L .