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

Abstract

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. © 2007 Springer-Verlag.