TY - JOUR
T1 - Anti-self-duality of curvature and degeneration of metrics with special holonomy
AU - Cheeger, Jeff
AU - Tian, Gang
PY - 2005/4
Y1 - 2005/4
N2 - 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.
AB - 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.
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U2 - 10.1007/s00220-004-1279-0
DO - 10.1007/s00220-004-1279-0
M3 - Article
AN - SCOPUS:15244352071
SN - 0010-3616
VL - 255
SP - 391
EP - 417
JO - Communications In Mathematical Physics
JF - Communications In Mathematical Physics
IS - 2
ER -