Publications
2002
Issue 73

MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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

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Received:: 28.08.02

Published:: 28.08.02

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

BibTex DOI: 10.1090/S0002-9947-02-03132-X