- 264 Downloads
Schur’s lemma states that every Einstein manifold of dimension n ≥ 3 has constant scalar curvature. 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. In particular, we provide an optimal L2 estimate under suitable assumptions and show that these assumptions cannot be removed.
Mathematics Subject Classification (2000)53C21 53C24
Unable to display preview. Download preview PDF.
- 2.Ge, Y., Wang, G.: An almost Schur theorem on 4-dimensional manifolds. Preprint 2010Google Scholar
- 5.Perez, D.: PhD thesis, Universität Zürich. In preparationGoogle Scholar
- 6.Thurston, W.P.: Hyperbolic structures on 3-manifolds II: surface groups and 3-manifolds which fibre over the circle. arXiv:math.GT/9801045Google Scholar
- 7.Topping, P.M.: Lectures on the Ricci flow. L.M.S. Lecture note series, vol. 325, C.U.P. (2006). http://www.warwick.ac.uk/~maseq/RFnotes.html