Prescribed Q-curvature problem on closed 4-Riemannian manifolds in the null case

Yuxin Ge (1) , Xingwang Xu

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

The main objective of this short note is to give a sufficient condition for a non constant function k to be Q curvature candidate for a conformal metric on a closed Riemannian manifold with the null Q-curvature. In contrast to the prescribed scalar curvature on the two-dimensional flat tori, the condition we provided is not necessary as some examples show.

Domaines: Physique mathématique [math-ph]

Yuxin Ge, Xingwang Xu. Prescribed Q-curvature problem on closed 4-Riemannian manifolds in the null case. Calculus of Variations and Partial Differential Equations, 2008, 31 (4), pp.549--555. ⟨10.1007/s00526-007-0130-9⟩. ⟨hal-00693073⟩