Inversion d'op\'erateurs de courbure au voisinage d'une m\'etrique Ricci parall\`ele

TL;DR

This paper investigates the invertibility of certain operators related to Ricci curvature on compact Riemannian manifolds with parallel Ricci curvature, demonstrating local invertibility near the given metric.

Contribution

It establishes the local invertibility of Ricci-affine operators near a metric with parallel Ricci curvature, advancing understanding of geometric operator behavior.

Findings

Operators affine to Ricci curvature are locally invertible near the metric g.

The result applies to compact Riemannian manifolds without boundary.

The study provides new insights into the structure of Ricci-related geometric operators.

Abstract

Let $(M,g)$ be a compact riemannian manifold without boundary., with parallel Rici curvature. We show that some operators, affine relatively to the Ricci curvature,are locally invertible, near the metric $g$