Partial Differential Equations
A Kazdan–Warner type identity for the σk curvature
Comptes Rendus. Mathématique, Volume 342 (2006) no. 7, pp. 475-478.

We prove a Kazdan–Warner type identity involving the σk 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.

Nous prouvons une identité de type Kazdan–Warner reliant la σk-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.

Received:
Published online:
DOI: 10.1016/j.crma.2006.01.023
Han, Zheng-Chao 1

1 Department of Mathematics, Rutgers University, 110, Frelinghuysen Road, Piscataway, NJ 08854, USA
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Han, Zheng-Chao. 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. http://www.numdam.org/articles/10.1016/j.crma.2006.01.023/

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