TY - JOUR
T1 - Bach-flat asymptotically locally Euclidean metrics
AU - Tian, Gang
AU - Viaclovsky, Jeff
PY - 2005/5
Y1 - 2005/5
N2 - We obtain a volume growth and curvature decay result for various classes of complete, noncompact Riemannian metrics in dimension 4; in particular our method applies to anti-self-dual or Kähler metrics with zero scalar curvature, and metrics with harmonic curvature. Similar results were obtained for Einstein metrics in [And89], [BKN89], [Tia90], but our analysis differs from the Einstein case in that (1) we consider more generally a fourth order system in the metric, and (2) we do not assume any pointwise Ricci curvature bound.
AB - We obtain a volume growth and curvature decay result for various classes of complete, noncompact Riemannian metrics in dimension 4; in particular our method applies to anti-self-dual or Kähler metrics with zero scalar curvature, and metrics with harmonic curvature. Similar results were obtained for Einstein metrics in [And89], [BKN89], [Tia90], but our analysis differs from the Einstein case in that (1) we consider more generally a fourth order system in the metric, and (2) we do not assume any pointwise Ricci curvature bound.
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U2 - 10.1007/s00222-004-0412-1
DO - 10.1007/s00222-004-0412-1
M3 - Article
AN - SCOPUS:17444402507
SN - 0020-9910
VL - 160
SP - 357
EP - 415
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
IS - 2
ER -