Soit une variété riemannienne compacte sans bord, à courbure de Ricci parallèle. Nous montrons que certains opérateurs, affines en la courbure de Ricci, sont localement inversibles, au voisinage de la métrique .
Let be a compact riemannian manifold without boundary, with parallel Ricci curvature. We show that some operators, affine relatively to the Ricci curvature, are locally invertible, near the metric .
Accepté le : 2016-07-12
Publié le : 2017-05-31
Classification : 53C21, 53A45, 58J05, 58J37, 35J62
Mots clés : Courbure de Ricci, variété produit, métriques d’Einstein, 2-tenseurs symétriques, EDP elliptique quasi-linéaire.
@article{AIF_2017__67_2_521_0, author = {Delay, Erwann}, title = {Inversion d'op\'erateurs de courbure au voisinage d'une m\'etrique Ricci parall\`ele}, journal = {Annales de l'Institut Fourier}, pages = {521--538}, publisher = {Association des Annales de l'institut Fourier}, volume = {67}, number = {2}, year = {2017}, doi = {10.5802/aif.3090}, language = {fr}, url = {https://aif.centre-mersenne.org/item/AIF_2017__67_2_521_0/} }
Delay, Erwann. Inversion d’opérateurs de courbure au voisinage d’une métrique Ricci parallèle. Annales de l'Institut Fourier, Tome 67 (2017) no. 2, pp. 521-538. doi : 10.5802/aif.3090. https://aif.centre-mersenne.org/item/AIF_2017__67_2_521_0/
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