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MiS Preprint
73/2002

Some properties of the Schouten tensor and applications to conformal geometry

Pengfei Guan, Jeff Viaclovsky and Guofang Wang

Abstract

In this paper, we prove that positive $\Gamma_k$-curvature for any $k\ge n/2$ implies positive Ricci curvature. Hence a compact locally conformally flat manifold with positive $\Gamma_k$-curvature ($k\ge n/2$) is a space form. And we prove some conformal quermassintegral inequalities, which are analogous to the classical quermassintegral inequalities in convex geometry.

Received:
Aug 28, 2002
Published:
Aug 28, 2002
MSC Codes:
53C21, 35J60, 58E11
Keywords:
$\gamma_k$-curvature, ricci curvature, conformal deformation

Related publications

inJournal
2003 Repository Open Access
Pengfei Guan, Jeff Viaclovsky and Guofang Wang

Some properties of the Schouten tensor and applications to conformal geometry

In: Transactions of the American Mathematical Society, 355 (2003) 3, pp. 925-933