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A fully nonlinear equation on 4-manifolds with positive scalar curvature

Matthew Gursky·Jeff Viaclovsky
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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 $Q$-curvature.

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Matthew Gursky, Jeff Viaclovsky. 2003-06-09. A fully nonlinear equation on 4-manifolds with positive scalar curvature. https://arxiv.org/abs/math/0301350

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