Min-Oo, Maung Almost Einstein manifolds of negative Ricci curvature. (English) Zbl 0725.53050 J. Differ. Geom. 32, No. 2, 457-472 (1990). By the technique used to deform the metric in the direction of its Ricci curvature, first done by R. S. Hamilton [Differ. Geom. 17, 255-306 (1982; Zbl 0504.53034)], the author proves the following pinching theorem for the Ricci curvature. Theorem: For any \(n\geq 3\) and \(\Lambda >0\), there exists an \(e(n,\Lambda)\), depending only on n and \(\Lambda\), such that if \((M^ n,g)\in M^-(m,\Lambda)\) and if its Ricci curvature satisfies \(\max_{SM} | n\rho /r-1| <\epsilon(n,\Lambda),\) then M admits an Einstein metric \(\bar g\) with \(\rho(\bar g)\equiv -1\), where \(M^-(n,\Lambda)\) denotes the set of all smooth compact Riemannian manifolds \((M^ n,g)\) satisfying) \(r<0\) and \(d^ 2 \max | K| \leq \Lambda^ 2\). Reviewer: H.Özekes (İstanbul) Cited in 1 ReviewCited in 4 Documents MSC: 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) Keywords:pinching theorem; Ricci curvature; Einstein metric Citations:Zbl 0504.53034 PDFBibTeX XMLCite \textit{M. Min-Oo}, J. Differ. Geom. 32, No. 2, 457--472 (1990; Zbl 0725.53050) Full Text: DOI