An Equation of Monge-Ampère Type in Conformal Geometry, and Four-Manifolds of Positive Ricci Curvature

We formulate natural conformally invariant conditions on a 4-manifold for the existence of a metric whose Schouten tensor satisfies a quadratic inequality. This inequality implies that the eigenvalues of the Ricci tensor are positively pinched.

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Bibliographic Details
Published in:	Annals of mathematics Vol. 155; no. 3; pp. 709 - 787
Main Authors:	Chang, Sun-Yung A., Gursky, Matthew J., Yang, Paul C.
Format:	Journal Article
Language:	English
Published:	Princeton, NJ Princeton University Press 01-05-2002
Subjects:	A priori knowledge Curvature Differential geometry Eigenvalues Exact sciences and technology Geometry Laplacians Mathematical inequalities Mathematics Riemann manifold Scalars Sciences and techniques of general use Tensors Conformal theory Invariant Riemann manifold Tensor Manifold Differential geometry Ricci curvature Yamabe invariant Compact surface Curvature Ricci tensor Gauss Bonnet formula
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Description
Summary:	We formulate natural conformally invariant conditions on a 4-manifold for the existence of a metric whose Schouten tensor satisfies a quadratic inequality. This inequality implies that the eigenvalues of the Ricci tensor are positively pinched.
ISSN:	0003-486X 1939-8980
DOI:	10.2307/3062131