Anti-self-duality of curvature and degeneration of metrics with special holonomy

Jeff Cheeger, Gang Tian

Research output: Contribution to journalArticle

Abstract

We study the structure of noncollapsed Gromov-Hausdorff limits of sequences, Min, of riemannian manifolds with special holonomy. We show that these spaces are smooth manifolds with special holonomy off a closed subset of codimension ≥4. Additional results on the the detailed structure of the singular set support our main conjecture that if the M in are compact and a certain characteristic number, C(Min), is bounded independent of i, then the singularities are of orbifold type off a subset of real codimension at least 6.

Original languageEnglish (US)
Pages (from-to)391-417
Number of pages27
JournalCommunications in Mathematical Physics
Volume255
Issue number2
DOIs
StatePublished - Apr 2005

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Self-duality
degeneration
Holonomy
Degeneration
Codimension
set theory
Curvature
curvature
Characteristic numbers
Metric
Singular Set
Subset
Smooth Manifold
Orbifold
Riemannian Manifold
Singularity
Closed

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

Anti-self-duality of curvature and degeneration of metrics with special holonomy. / Cheeger, Jeff; Tian, Gang.

In: Communications in Mathematical Physics, Vol. 255, No. 2, 04.2005, p. 391-417.

Research output: Contribution to journalArticle

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