An almost-Schur type lemma for symmetric (2,0) tensors and applications

Xu Cheng

Vol. 267 (2014), No. 2, 325–340

DOI: 10.2140/pjm.2014.267.325

Abstract

In a previous paper, we generalized the almost-Schur lemma of De Lellis and Topping for closed manifolds with nonnegative Ricci curvature to any closed manifolds. In this paper, we generalize the above results to symmetric $\left(2,0\right)$-tensors and give the applications for $r$-th mean curvatures of closed hypersurfaces in space forms and $k$ scalar curvatures for closed locally conformally flat manifolds.

Keywords

traceless tensor, Ricci curvature, mean curvature

Mathematical Subject Classification 2010

Primary: 53C21

Milestones

Received: 21 September 2012

Revised: 19 February 2013

Accepted: 6 May 2013

Published: 11 May 2014