A fully nonlinear equation on 4-manifolds with positive scalar curvature
Differential Geometry
2009-08-26 v3 Analysis of PDEs
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.
Cite
@article{arxiv.math/0301350,
title = {A fully nonlinear equation on 4-manifolds with positive scalar curvature},
author = {Matthew Gursky and Jeff Viaclovsky},
journal= {arXiv preprint arXiv:math/0301350},
year = {2009}
}
Comments
20 pages; to appear in Journal of Differential Geometry