A fully nonlinear equation on 4-manifolds with positive scalar curvature
arXiv:math/0301350
Abstract
We present a conformal deformation involving a fully nonlinear equation in dimension 4, starting with positive scalar curvature. Assuming a certain conformal invariant is positive, one may deform from positive scalar curvature to a stronger condition involving the Ricci tensor. We also give a new conformally invariant condition for positivity of the Paneitz operator, which allows us to give many new examples of manifolds admitting metrics with constant -curvature.
20 pages; to appear in Journal of Differential Geometry