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

Jeff Cheeger; Gang Tian

doi:10.1007/s00220-004-1279-0

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

Jeff Cheeger, Gang Tian

Mathematics

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

We study the structure of noncollapsed Gromov-Hausdorff limits of sequences, M_iⁿ, 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(M_iⁿ), is bounded independent of i, then the singularities are of orbifold type off a subset of real codimension at least 6.

Original language	English (US)
Pages (from-to)	391-417
Number of pages	27
Journal	Communications In Mathematical Physics
Volume	255
Issue number	2
DOIs	https://doi.org/10.1007/s00220-004-1279-0
State	Published - Apr 2005

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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

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