Some properties of the Schouten tensor and applications to conformal geometry

Pengfei Guan, Jeff Viaclovsky, and Guofang Wang
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Submission date: 28. Aug. 2002
Pages: 13
published in: Transactions of the American Mathematical Society, 355 (2003) 3, p. 925-933 
MSC-Numbers: 53C21, 35J60, 58E11
Keywords and phrases: $\gamma_k$-curvature, ricci curvature, conformal deformation
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Abstract:
In this paper, we prove that positive -curvature for any implies positive Ricci curvature. Hence a compact locally conformally flat manifold with positive -curvature () is a space form. And we prove some conformal quermassintegral inequalities, which are analogous to the classical quermassintegral inequalities in convex geometry.