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Let (M,g) be a complete noncompact riemannian manifold with bounded geometryand parallel Ricci curvature. We show that some operators, "affine" relativelyto the Ricci curvature, are locally invertible, in some classical Sobolevspaces, near the metric g.

Inversion of some curvature operators near a parallel Ricci metric II: Non-compact manifold with bounded geometry