The Einstein-Maxwell equations, Kähler metrics, and Hermitian geometry

Claude LeBrun

doi:10.1016/j.geomphys.2015.01.009

The Einstein-Maxwell equations, Kähler metrics, and Hermitian geometry

Claude LeBrun

Mathematics

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

26 Scopus citations

Abstract

Any constant-scalar-curvature Kähler (cscK) metric on a complex surface may be viewed as a solution of the Einstein-Maxwell equations, and this allows one (LeBrun, 2010; Shu, 2009) to produce solutions of these equations on any 4-manifold that arises as a compact complex surface with b1even. However, not all solutions of the Einstein-Maxwell equations on such manifolds arise in this way; new examples can be constructed by means of conformally Kähler geometry.

Original language	English
Pages (from-to)	163-171
Number of pages	9
Journal	Journal of Geometry and Physics
Volume	91
DOIs	https://doi.org/10.1016/j.geomphys.2015.01.009
State	Published - May 1 2015

Keywords

Conformal
Einstein-Maxwell
Hermitian
Kähler
Riemannian

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10.1016/j.geomphys.2015.01.009

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abstract = "Any constant-scalar-curvature K{\"a}hler (cscK) metric on a complex surface may be viewed as a solution of the Einstein-Maxwell equations, and this allows one (LeBrun, 2010; Shu, 2009) to produce solutions of these equations on any 4-manifold that arises as a compact complex surface with b1even. However, not all solutions of the Einstein-Maxwell equations on such manifolds arise in this way; new examples can be constructed by means of conformally K{\"a}hler geometry.",

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author = "Claude LeBrun",

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AB - Any constant-scalar-curvature Kähler (cscK) metric on a complex surface may be viewed as a solution of the Einstein-Maxwell equations, and this allows one (LeBrun, 2010; Shu, 2009) to produce solutions of these equations on any 4-manifold that arises as a compact complex surface with b1even. However, not all solutions of the Einstein-Maxwell equations on such manifolds arise in this way; new examples can be constructed by means of conformally Kähler geometry.

KW - Conformal

KW - Einstein-Maxwell

KW - Hermitian

KW - Kähler

KW - Riemannian

UR - https://www.scopus.com/pages/publications/84939979927

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VL - 91

SP - 163

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JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

ER -

The Einstein-Maxwell equations, Kähler metrics, and Hermitian geometry

Abstract

Keywords

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