Coupled equations for Kähler metrics and Yang-Mills connections

@article{GarciaFernandez2013CoupledEF,
  title={Coupled equations for K{\"a}hler metrics and Yang-Mills connections},
  author={Mario Garcia-Fernandez},
  journal={Geometry & Topology},
  year={2013},
  volume={17},
  pages={2731-2812}
}
  • Mario Garcia-Fernandez
  • Published 2013
  • Mathematics, Physics
  • Geometry & Topology
  • We study equations on a principal bundle over a compact complex manifold coupling a connection on the bundle with a Kahler structure on the base. These equations generalize the conditions of constant scalar curvature for a Kahler 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… CONTINUE READING

    Citations

    Publications citing this paper.
    SHOWING 1-10 OF 17 CITATIONS

    Deformation of complex structures and the coupled Kähler-Yang-Mills equations

    VIEW 5 EXCERPTS
    CITES METHODS & BACKGROUND

    On coupled constant scalar curvature K\"ahler metrics

    VIEW 3 EXCERPTS
    CITES METHODS & BACKGROUND
    HIGHLY INFLUENCED

    Coupled equations for Kähler metrics and Yang-Mills connections

    VIEW 3 EXCERPTS
    CITES BACKGROUND & METHODS

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 107 REFERENCES

    Symmetric Spaces

    VIEW 21 EXCERPTS
    HIGHLY INFLUENTIAL

    K-ENERGY MAPS INTEGRATING FUTAKI INYARIANTS

    VIEW 11 EXCERPTS
    HIGHLY INFLUENTIAL

    Geometry of Yang-Mills fields

    VIEW 4 EXCERPTS
    HIGHLY INFLUENTIAL

    Hamiltonian 2forms in Kähler geometry

    • V. Apostolov, D. Calderbank, P. Gauduchon, W. Tønnesen-Friedman
    • III Extremal metrics and stability, Invent. Math 173
    • 2008
    VIEW 5 EXCERPTS
    HIGHLY INFLUENTIAL

    Remarks on gauge theory

    • S K Donaldson
    • complex geometry and 4–manifold topology, from: “Fields Medallists’ lectures”, (M F Atiyah, D Iagolnitzer, editors), World Sci. Ser. 20th Century Math. 5, World Sci. Publ.
    • 1997
    VIEW 17 EXCERPTS
    HIGHLY INFLUENTIAL

    Infinite determinants

    • S K Donaldson
    • stable bundles and curvature, Duke Math. J. 54
    • 1987
    VIEW 18 EXCERPTS
    HIGHLY INFLUENTIAL