Almost-Schur lemma

2010/03/18 by Camillo De Lellis, De Lellis, Camillo, Peter M. Topping +1 · 2 citations
Mathematics · Physics and Astronomy · #53C24 #58J99 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1003.3527

openalex publication_date 2010/03/18 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

Schur's lemma states that every Einstein manifold of dimension n≥ 3 has constant scalar curvature. Here (M,g) is defined to be Einstein if its traceless Ricci tensor \Rico:=\Ric-(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 small rather than identically zero.

Cited by

• An almost-almost-Schur lemma on the 3-sphere
• Topology at infinity of complete gradient Schouten solitons

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