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

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

2003-01-30

arxiv.org/abs/math/0301350v3

Final version: Journal of Differential Geometry 63, no. 1, 2003, 131-154

Mathematics

Differential Geometry

20 pages; to appear in Journal of Differential Geometry

Scientific paper

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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