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

TL;DR

This paper demonstrates local invertibility of certain affine operators related to Ricci curvature on complete noncompact manifolds with bounded geometry and parallel Ricci curvature, expanding understanding of geometric analysis in noncompact settings.

Contribution

It establishes the local invertibility of specific curvature-related operators on noncompact manifolds with bounded geometry and parallel Ricci curvature, extending previous results to noncompact cases.

Findings

Operators are locally invertible in Sobolev spaces near the given metric.

Invertibility holds for manifolds with bounded geometry and parallel Ricci curvature.

Results apply to a class of noncompact manifolds, broadening geometric analysis tools.

Abstract

Let (M,g) be a complete noncompact riemannian manifold with bounded geometry and parallel Ricci curvature. We show that some operators, "affine" relatively to the Ricci curvature, are locally invertible, in some classical Sobolev spaces, near the metric g.