Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.
Some properties of the Schouten tensor and applications to conformal geometry
Pengfei Guan, Jeff Viaclovsky and Guofang Wang
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.