A remark on the nonnegativity of the Paneitz operator

Abstract

In this short article, we interpret the condition of a theorem of Gursky-Viaclovsky concerning the nonnegativity of the Paneitz operator as the metric being 3 3 -positive Ricci. By a result of Wolfson, this condition can be preserved under the surgery of codimension q ≥ 3 q\geq 3 . Combining these two observations, we expand the list of manifolds which admit metrics with a nonnegative Paneitz operator. Consequently, there exist metrics of constant Q Q -curvature on these manifolds.