Anti-self-duality of curvature and degeneration of metrics with special holonomy
type: Item
instance of: scholarly article
title: Anti-self-duality of curvature and degeneration of metrics with special holonomy
zbMATH Open document ID: 1081.53038
author: Jeff Cheeger
author: Gang Tian
published in: Communications in Mathematical Physics
publication date: 2005-06-08T00:00:00Z
review text: The authors study the structure of non-collapsed Gromov-Hausdorff limits of sequences, \(M_i^n\), of Riemannian manifolds with special holonomy. They prove that these spaces are smooth manifolds with special holonomy off a closed subset of codimension \(\geq 4\). If, in addition, the manifolds are compact and the sequence of certain characteristic numbers, \(C(M_i)\), is bounded, the authors obtain detailed information about the singular set. These results support the authors' conjecture that off a closed subset of codimension at least \(6\), the singularities are of orbifold type and the orbifold structure is compatible with the holonomy group.
reviewed by: Mingliang Cai
Mathematics Subject Classification ID: 53C23
Mathematics Subject Classification ID: 53C29
zbMATH DE Number: 2174471
zbMATH Keywords: Gromov-Hausdorff limit
zbMATH Keywords: special holonomy
zbMATH Keywords: anti-self-duality of curvature
MaRDI profile type: Publication
full work available at URL: s00220-004-1279-0
OpenAlex ID: W2087578610
cites work: A Theorem on Holonomy
cites work: Ricci Curvature Bounds and Einstein Metrics on Compact Manifolds
cites work: Convergence and rigidity of manifolds under Ricci curvature bounds
cites work: The \(L^ 2\) structure of moduli spaces of Einstein metrics on 4- manifolds
cites work: Q4865992
cites work: Q4474315
cites work: Special quantum field theories in eight and other dimensions
cites work: Sur les groupes d'holonomie homogènes de variétés à connexion affine et des variétés riemanniennes
cites work: Q4720334
cites work: Q5657335
cites work: Differentiability of Lipschitz functions on metric measure spaces
cites work: \(L_p\)-bounds on curvature, elliptic estimates and rectifiability of singular sets
cites work: Q4449312
cites work: Integral bounds on curvature, elliptic estimates and rectifiability of singular sets
cites work: Q4463914
cites work: Q4852335
cites work: Lower bounds on Ricci curvature and the almost rigidity of warped products
cites work: On the structure of spaces with Ricci curvature bounded below. I
cites work: On the structure of spaces with Ricci curvature bounded below. II
cites work: On the structure of spaces with Ricci curvature bounded below. III
cites work: Constraints on singularities under Ricci curvature bounds
cites work: On the singularities of spaces with bounded Ricci curvature
cites work: Shape of manifolds with positive Ricci curvature
cites work: Large manifolds with positive Ricci curvature
cites work: Ricci curvature and volume convergence
cites work: Q4850454
cites work: Quaternion Kählerian manifolds
cites work: Q4523708
cites work: Characteristic Classes. (AM-76)
cites work: Q3802189
cites work: Q4084319
cites work: Q3995081
cites work: Quaternion-Kähler geometry
cites work: On the transitivity of holonomy systems
cites work: On Calabi's conjecture for complex surfaces with positive first Chern class
cites work: Q4503254
cites work: Gauge theory and calibrated geometry. I
DOI: 10.1007/S00220-004-1279-0
Recommended article: Q4463914
Recommended article: Q4865998
Recommended article: Einstein metrics, conformal curvature, and anti-holomorphic involutions
Recommended article: Anti-self-dual equation on 4-manifolds with degenerate metric
Recommended article: Ricci-flat deformations of metrics with exceptional holonomy
Recommended article: Toric anti-self-dual Einstein metrics via complex geometry
Recommended article: The deformation theory of anti-self-dual conformal structures
Recommended article: Almost-Kähler anti-self-dual metrics
Recommended article: Q4036989
Recommended article: On the scalar curvature of self-dual manifolds
description: scientific article; zbMATH DE number 2174471