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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.
