Some properties of the Schouten tensor and applications to conformal geometry
Pengfei Guan, Jeff Viaclovsky, and Guofang Wang
Contact the author: Please use for correspondence this email.
Submission date: 28. Aug. 2002
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
Download full preprint: PDF (171 kB), PS ziped (190 kB)
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.