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Coupled equations for
Kähler metrics and Yang–Mills connections
Luis Álvarez-Cónsul, Mario García-Fernández and Oscar García-Prada |
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Geometry & Topology 17 (2013) 2731–2812
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Abstract |
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We study equations on a principal bundle over a compact complex manifold coupling a connection on the bundle with a Kähler structure on the base. These equations generalize the conditions of constant scalar curvature for a Kähler metric and Hermite–Yang–Mills for a connection. We provide a moment map interpretation of the equations and study obstructions for the existence of solutions, generalizing the Futaki invariant, the Mabuchi K–energy and geodesic stability. We finish by giving some examples of solutions. |
Keywords
coupled Kähler–Yang–Mills equation, Kähler metric,
Hermitian–Yang–Mills connection, generalized Futaki
invariant, generalized Mabuchi energy
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Mathematical Subject Classification 2010
Primary: 32Q20, 53C07
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References |
Publication
Received: 29 June 2012
Revised: 26 March 2013
Accepted: 25 April 2013
Published: 14 October 2013
Proposed: Simon Donaldson
Seconded: Richard Thomas, Frances Kirwan
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Authors |
| Luis Álvarez-Cónsul | |
| Instituto de Ciencias
Matemáticas C/ Nicolás Cabrera 13–15 Campus Cantoblanco 28049 Madrid Spain |
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| Mario García-Fernández | |
| MATHGEOM École Polytechnique Fédéral de Lausanne MA B1 437, Station 8 CH-1015 Lausanne Switzerland |
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| Oscar García-Prada | |
| Instituto de Ciencias Matemáticas
(CSIC-UAM-UC3M-UCM) C/ Nicolás Cabrera 13–15 Campus Cantoblanco 28049 Madrid Spain |
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