Hausdorff perturbations of Ricci-flat manifolds and the splitting theorem

DOI10.1215/S0012-7094-92-06803-7zbMath0767.53029MaRDI QIDQ1202446

Michael T. Anderson

Publication date: 2 February 1993

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

Gromov-Hausdorff topologySchwarzschild metricCheeger-Gromoll global splitting theoremcollapsing Ricci-flat manifoldGromoll-Yamaguchi conjectureminimizing geodesicToponogov splitting

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20)

Related Items (18)

Collapsing and Almost Nonnegative Curvature ⋮ Smoothing Riemannian metrics with Ricci curvature bounds ⋮ The collapsing geometry of almost Ricci-flat 4-manifolds ⋮ Fibrations and stability for compact group actions on manifolds with local bounded Ricci covering geometry ⋮ Regularity of Einstein manifolds and the codimension 4 conjecture ⋮ Almost nonnegative Ricci curvature and new vanishing theorems for genera ⋮ Structure theory and convergence in Riemannian geometry ⋮ On clusters and the multi-isoperimetric profile in Riemannian manifolds with bounded geometry ⋮ Kummer-type constructions of almost Ricci-flat 5-manifolds ⋮ Collapsed manifolds with Ricci bounded covering geometry ⋮ \(L^2\) curvature bounds on manifolds with bounded Ricci curvature ⋮ On Fox's \(m\)-dimensional category and theorems of Bochner type ⋮ Collapsed Ricci limit spaces as non-collapsed RCD spaces ⋮ Local Splitting Theorems for Riemannian Manifolds ⋮ Nilpotency, almost nonnegative curvature, and the gradient flow on Alexandrov spaces ⋮ Morse-Novikov cohomology of almost nonnegatively curved manifolds ⋮ Ricci curvature and Betti numbers ⋮ Manifolds of almost nonnegative curvature

Cites Work

• The construction of negatively Ricci curved manifolds
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• Collapsing and pinching under a lower curvature bound
• Diffeomorphism finiteness for manifolds with Ricci curvature and \(L^{n/2}\)-norm of curvature bounded
• The fundamental groups of almost nonnegatively curved manifolds
• Ricci curvature, diameter and optimal volume bound
• Métriques riemanniennes et courbure
• The splitting theorem for manifolds of nonnegative Ricci curvature
• On Complete Manifolds With Nonnegative Ricci Curvature
• A compactification of a manifold with asymptotically nonnegative curvature
• A.D. Alexandrov spaces with curvature bounded below
• Riemannian spaces which contain straight lines
• Almost flat manifolds
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