Einstein metrics, symplectic minimality, and pseudo-holomorphic curves

Claude Lebrun

doi:10.1007/s10455-005-3892-5

Einstein metrics, symplectic minimality, and pseudo-holomorphic curves

Claude Lebrun

Mathematics

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

8 Scopus citations

Abstract

Let (M ⁴, g,ω) be a compact, almost-Kähler-Einstein manifold of negative star-scalar curvature. Then (M,ω) is a minimal symplectic 4-manifold of general type. In particular, M cannot be differentiably decomposed as a connected sum N#ℂℙ₂.

Original language	English
Pages (from-to)	157-177
Number of pages	21
Journal	Annals of Global Analysis and Geometry
Volume	28
Issue number	2
DOIs	https://doi.org/10.1007/s10455-005-3892-5
State	Published - Sep 2005

Keywords

Einstein manifold
Pseudo-holomorphic curve
Symplectic manifold

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10.1007/s10455-005-3892-5

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title = "Einstein metrics, symplectic minimality, and pseudo-holomorphic curves",

abstract = "Let (M 4, g,ω) be a compact, almost-K{\"a}hler-Einstein manifold of negative star-scalar curvature. Then (M,ω) is a minimal symplectic 4-manifold of general type. In particular, M cannot be differentiably decomposed as a connected sum N\#ℂℙ2.",

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AU - Lebrun, Claude

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N2 - Let (M 4, g,ω) be a compact, almost-Kähler-Einstein manifold of negative star-scalar curvature. Then (M,ω) is a minimal symplectic 4-manifold of general type. In particular, M cannot be differentiably decomposed as a connected sum N#ℂℙ2.

AB - Let (M 4, g,ω) be a compact, almost-Kähler-Einstein manifold of negative star-scalar curvature. Then (M,ω) is a minimal symplectic 4-manifold of general type. In particular, M cannot be differentiably decomposed as a connected sum N#ℂℙ2.

KW - Einstein manifold

KW - Pseudo-holomorphic curve

KW - Symplectic manifold

UR - https://www.scopus.com/pages/publications/26844446397

U2 - 10.1007/s10455-005-3892-5

DO - 10.1007/s10455-005-3892-5

M3 - Article

AN - SCOPUS:26844446397

SN - 0232-704X

VL - 28

SP - 157

EP - 177

JO - Annals of Global Analysis and Geometry

JF - Annals of Global Analysis and Geometry

IS - 2

ER -

Einstein metrics, symplectic minimality, and pseudo-holomorphic curves

Abstract

Keywords

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