Bach-flat asymptotically locally Euclidean metrics

Details Bach-flat asymptotically locally Euclidean metrics Bach-flat asymptotically locally Euclidean metrics

2003-10-19

arxiv.org/abs/math/0310302v3

Inventiones Mathematicae 160 (2), 2005, pages 357-415

Mathematics

Differential Geometry

54 pages; final version

Scientific paper

10.1007/s00222-004-0412-1

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 Kahler metrics with zero scalar curvature, and metrics with harmonic curvature. Similar results are known for Einstein metrics, 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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