Almost-Schur lemma

Details Almost-Schur lemma Almost-Schur lemma

2010-03-18

arxiv.org/abs/1003.3527v2

Mathematics

Differential Geometry

Remarks and references added. To appear in Calc. Var. See also http://www.math.uzh.ch/delellis

Scientific paper

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.

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