On the scalar curvature of Einstein manifolds

Fabrizio Catanese; Claude LeBrun

doi:10.4310/MRL.1997.v4.n6.a5

On the scalar curvature of Einstein manifolds

Fabrizio Catanese
, Claude LeBrun

Mathematics

Stony Brook University

Mathematisches Institut

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

27 Scopus citations

Abstract

We show that there are high-dimensional smooth compact manifolds which admit pairs of Einstein metrics for which the scalar curvatures have opposite signs. These are counter-examples to a conjecture considered by Besse [6, p. 19]. The proof hinges on showing that the Barlow surface has small deformations with ample canonical line bundle.

Original language	English
Pages (from-to)	843-854
Number of pages	12
Journal	Mathematical Research Letters
Volume	4
Issue number	6
DOIs	https://doi.org/10.4310/MRL.1997.v4.n6.a5
State	Published - 1997

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10.4310/MRL.1997.v4.n6.a5

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title = "On the scalar curvature of Einstein manifolds",

abstract = "We show that there are high-dimensional smooth compact manifolds which admit pairs of Einstein metrics for which the scalar curvatures have opposite signs. These are counter-examples to a conjecture considered by Besse [6, p. 19]. The proof hinges on showing that the Barlow surface has small deformations with ample canonical line bundle.",

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AU - LeBrun, Claude

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AB - We show that there are high-dimensional smooth compact manifolds which admit pairs of Einstein metrics for which the scalar curvatures have opposite signs. These are counter-examples to a conjecture considered by Besse [6, p. 19]. The proof hinges on showing that the Barlow surface has small deformations with ample canonical line bundle.

UR - https://www.scopus.com/pages/publications/0031283712

U2 - 10.4310/MRL.1997.v4.n6.a5

DO - 10.4310/MRL.1997.v4.n6.a5

M3 - Article

SN - 1073-2780

VL - 4

SP - 843

EP - 854

JO - Mathematical Research Letters

JF - Mathematical Research Letters

IS - 6

ER -

On the scalar curvature of Einstein manifolds

Abstract

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