Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 20 (2024), 032, 13 pages      arXiv:2309.15673      https://doi.org/10.3842/SIGMA.2024.032
Contribution to the Special Issue on Differential Geometry Inspired by Mathematical Physics in honor of Jean-Pierre Bourguignon for his 75th birthday

Kähler-Yang-Mills Equations and Vortices

Oscar García-Prada
Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM),Nicolás Cabrera 13-15, Cantoblanco, 28049 Madrid, Spain

Received October 02, 2023, in final form April 04, 2024; Published online April 11, 2024

Abstract
The Kähler-Yang-Mills equations are coupled equations for a Kähler metric on a compact complex manifold and a connection on a complex vector bundle over it. After briefly reviewing the main aspects of the geometry of the Kähler-Yang-Mills equations, we consider dimensional reductions of the equations related to vortices — solutions to certain Yang-Mills-Higgs equations.

Key words: Kähler-Yang-Mills equations; vortices; gravitating vortices; dimensional reduction; stability.

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