On optimal 4-dimensional metrics

Claude Lebrun; Bernard Maskit

doi:10.1007/s12220-008-9019-x

On optimal 4-dimensional metrics

Claude Lebrun
, Bernard Maskit

Mathematics

Stony Brook University

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

14 Scopus citations

Abstract

We completely determine, up to homeomorphism, which simply connected compact oriented 4-manifolds admit scalar-flat, anti-self-dual Riemannian metrics. The key new ingredient is a proof that the connected sum ℂℙ ₂#ℂℙ ₂#ℂℙ ₂#ℂℙ ₂#ℂℙ ₂ of five reverse-oriented complex projective planes admits such metrics.

Original language	English
Pages (from-to)	537-564
Number of pages	28
Journal	Journal of Geometric Analysis
Volume	18
Issue number	2
DOIs	https://doi.org/10.1007/s12220-008-9019-x
State	Published - Apr 2008

Keywords

4-manifold
Anti-self-dual metric
Kleinian group
Scalar curvature

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10.1007/s12220-008-9019-x

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abstract = "We completely determine, up to homeomorphism, which simply connected compact oriented 4-manifolds admit scalar-flat, anti-self-dual Riemannian metrics. The key new ingredient is a proof that the connected sum ℂℙ 2\#ℂℙ 2\#ℂℙ 2\#ℂℙ 2\#ℂℙ 2 of five reverse-oriented complex projective planes admits such metrics.",

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AB - We completely determine, up to homeomorphism, which simply connected compact oriented 4-manifolds admit scalar-flat, anti-self-dual Riemannian metrics. The key new ingredient is a proof that the connected sum ℂℙ 2#ℂℙ 2#ℂℙ 2#ℂℙ 2#ℂℙ 2 of five reverse-oriented complex projective planes admits such metrics.

KW - 4-manifold

KW - Anti-self-dual metric

KW - Kleinian group

KW - Scalar curvature

UR - https://www.scopus.com/pages/publications/84867934124

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JF - Journal of Geometric Analysis

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ER -

On optimal 4-dimensional metrics

Abstract

Keywords

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