[Une identité de type Kazdan–Warner pour la -courbure]
Nous prouvons une identité de type Kazdan–Warner reliant la -courbure et un champ de vecteurs conforme sur une variété compacte. Notre méthode permet aussi de fournir une preuve unifiée pour les conditions nécessaires dans le problème de Christoffel–Minkowski.
We prove a Kazdan–Warner type identity involving the curvature and a conformal Killing vector field on a compact manifold. Our method also works to provide a unified proof for the necessary conditions in the Christoffel–Minkowski problem.
@article{CRMATH_2006__342_7_475_0,
author = {Zheng-Chao Han},
title = {A {Kazdan{\textendash}Warner} type identity for the $ {\sigma }_{k}$ curvature},
journal = {Comptes Rendus. Math\'ematique},
pages = {475--478},
publisher = {Elsevier},
volume = {342},
number = {7},
year = {2006},
doi = {10.1016/j.crma.2006.01.023},
language = {en},
}
Zheng-Chao Han. A Kazdan–Warner type identity for the $ {\sigma }_{k}$ curvature. Comptes Rendus. Mathématique, Volume 342 (2006) no. 7, pp. 475-478. doi : 10.1016/j.crma.2006.01.023. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.01.023/
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