# Sur l'inversion de l'opérateur de Ricci au voisinage d'une métrique Ricci parallèle

Abstract : Let $(M,g)$ be a compact riemannian manifold without boundary. Under some natural conditions on the curvature, the Lichnerowicz Laplacian $\Delta_L$ is non negative and its kernel is reduced to parallel tensors. We assume that the Ricci curvature is non degenerate and parallel, and that the first Betti number vanishes. We show that for all $R$ close enough to the Ricci tensor of $g$, there exist a metric close to $g$ with Ricci curvature is $R$, up to an additionnal small element in $\ker\Delta_L$. We then give some examples of products of Einstein manifolds that satisfies the hypothesis. We also study the Ricci contravariant operator together with some other curvature operators.
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https://hal-univ-avignon.archives-ouvertes.fr/hal-00974707
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Submitted on : Monday, April 7, 2014 - 1:07:03 PM
Last modification on : Tuesday, February 22, 2022 - 11:36:03 AM
Long-term archiving on: : Monday, July 7, 2014 - 11:16:30 AM

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RicciProduit.pdf
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### Identifiers

• HAL Id : hal-00974707, version 1
• ARXIV : 1404.1865

### Citation

Erwann Delay. Sur l'inversion de l'opérateur de Ricci au voisinage d'une métrique Ricci parallèle. 2014. ⟨hal-00974707v1⟩

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