The CR Almost Schur Lemma and the positivity conditions

A note on the Almost Schur lemma on smooth metric measure spaces

In this paper, we prove almost Schur Lemma on closed smooth metric measure spaces, which implies the results of X. Cheng and De Lellis-Topping whenever the weighted function f is constant.

A generalization of almost Schur lemma on CR manifolds

In this paper, we study a general almost Schur Lemma on pseudo-Hermitian (2n+1)-manifolds $(M,J,θ)$ for $n\geq2$. When the equality of almost Schur inequality holds, we derive the contact form $θ$ is pseudo-Einstein and the pseudo-Hermitian scalar curvature is constant.

强可分解正向量丛的 Schur 形式的正性

Positivity of Schur forms for strongly decomposably positive vector bundles

本文定义两类强于 Finski 可分解正性的强可分解正性，给出判别准则并证明相应 Schur 形式的弱正性与正性，从而肯定回答 Griffiths 问题并代数重证 Nakano 情形。

The Almost Schur Lemma in Quaternionic Contact Geometry

We establish quaternionic contact (qc) versions of the so called Almost Schur Lemma, which give estimations of the qc scalar curvature on a compact qc manifold to be a constant in terms of the norm of the $[-1]$-component and the norm of the trace-free part of the $[3]$-component of the horizontal qc Ricci tensor and the torsion endomorphism, under certain positivity conditions.

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

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

Almost-Schur lemma

Schur's lemma states that every Einstein manifold of dimension $n\geq 3$ has constant scalar curvature. Here $(M,g)$ is defined to be Einstein if its traceless Ricci tensor $$\Rico:=\Ric-\frac{R}{n}g$$ is identically zero. In this short note we ask to what extent the scalar curvature is constant if the traceless Ricci tensor is assumed to be \emph{small} rather than identically zero.