Bach-flat asymptotically locally Euclidean metrics

• 成果类型: Article
• 署名作者: Tian, G; Viaclovsky, J
• 署名单位: Massachusetts Institute of Technology (MIT)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-004-0412-1
• 发表日期: 2005
• 页码: 357-415
• 关键词: positive scalar curvature; RIEMANNIAN-MANIFOLDS; einstein manifolds; volume growth; geometry; l-2-cohomology; SINGULARITIES; CONSTRUCTION; inequalities; conjecture

摘要

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 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.