Geometry & Topology

Coupled equations for Kähler metrics and Yang–Mills connections

Luis Álvarez-Cónsul, Mario García-Fernández, and Oscar García-Prada

Full-text: Open access

Abstract

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.

Article information

Source
Geom. Topol., Volume 17, Number 5 (2013), 2731-2812.

Dates
Received: 29 June 2012
Revised: 26 March 2013
Accepted: 25 April 2013
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513732687

Digital Object Identifier
doi:10.2140/gt.2013.17.2731

Mathematical Reviews number (MathSciNet)
MR3190298

Zentralblatt MATH identifier
1275.32019

Subjects
Primary: 32Q20: Kähler-Einstein manifolds [See also 53Cxx] 53C07: Special connections and metrics on vector bundles (Hermite-Einstein- Yang-Mills) [See also 32Q20]

Keywords
coupled Kähler–Yang–Mills equation Kähler metric Hermitian–Yang–Mills connection generalized Futaki invariant generalized Mabuchi energy

Citation

Álvarez-Cónsul, Luis; García-Fernández, Mario; García-Prada, Oscar. Coupled equations for Kähler metrics and Yang–Mills connections. Geom. Topol. 17 (2013), no. 5, 2731--2812. doi:10.2140/gt.2013.17.2731. https://projecteuclid.org/euclid.gt/1513732687


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