Bach-flat asymptotically locally Euclidean metrics

Gang Tian; Jeff Viaclovsky

doi:10.1007/s00222-004-0412-1

Bach-flat asymptotically locally Euclidean metrics

Gang Tian
, Jeff Viaclovsky

Mathematics

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

63 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	357-415
Number of pages	59
Journal	Inventiones Mathematicae
Volume	160
Issue number	2
DOIs	https://doi.org/10.1007/s00222-004-0412-1
State	Published - May 2005

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

10.1007/s00222-004-0412-1

Cite this

@article{985fde9b732c4b1e90dde47741e50da8,

title = "Bach-flat asymptotically locally Euclidean metrics",

abstract = "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 K{\"a}hler 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.",

author = "Gang Tian and Jeff Viaclovsky",

year = "2005",

month = may,

doi = "10.1007/s00222-004-0412-1",

language = "English (US)",

volume = "160",

pages = "357--415",

journal = "Inventiones Mathematicae",

issn = "0020-9910",

publisher = "Springer New York",

number = "2",

}

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.

UR - https://www.scopus.com/pages/publications/17444402507

UR - https://www.scopus.com/pages/publications/17444402507#tab=citedBy

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 -

Bach-flat asymptotically locally Euclidean metrics

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this