Nontrivial examples of coupled equations for Kähler metrics and Yang-Mills connections
Julien Keller ; Christina Tønnesen-Friedman
Open Mathematics, Tome 10 (2012), p. 1673-1687 / Harvested from The Polish Digital Mathematics Library

We provide nontrivial examples of solutions to the system of coupled equations introduced by M. García-Fernández for the uniformization problem of a triple (M; L; E), where E is a holomorphic vector bundle over a polarized complex manifold (M, L), generalizing the notions of both constant scalar curvature Kähler metric and Hermitian-Einstein metric.

Publié le : 2012-01-01
EUDML-ID : urn:eudml:doc:269378
@article{bwmeta1.element.doi-10_2478_s11533-012-0088-5,
     author = {Julien Keller and Christina T\o nnesen-Friedman},
     title = {Nontrivial examples of coupled equations for K\"ahler metrics and Yang-Mills connections},
     journal = {Open Mathematics},
     volume = {10},
     year = {2012},
     pages = {1673-1687},
     zbl = {1269.53049},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0088-5}
}
Julien Keller; Christina Tønnesen-Friedman. Nontrivial examples of coupled equations for Kähler metrics and Yang-Mills connections. Open Mathematics, Tome 10 (2012) pp. 1673-1687. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0088-5/

[1] Alvarez-Consul L., Garcia-Fernandez M., Garcia-Prada O., Coupled equations for Kähler metrics and Yang-Mills connections, preprint available at http://arxiv.org/abs/1102.0991 | Zbl 1275.32019

[2] Apostolov V., Calderbank D.M.J., Gauduchon P., Hamiltonian 2-forms in Kähler geometry I. General theory, J. Differential Geom., 2006, 73(3), 359–412 | Zbl 1101.53041

[3] Apostolov V., Calderbank D.M.J., Gauduchon P., Tønnesen-Friedman C.W., Hamiltonian 2-forms in Kähler geometry II. Global classification, J. Differential Geom., 2004, 68(2), 277–345 | Zbl 1079.32012

[4] Apostolov V., Calderbank D.M.J., Gauduchon P., Tønnesen-Friedman C.W., Hamiltonian 2-forms in Kähler geometry III. Extremal metrics and stability, Invent. Math., 2008, 173(3), 547–601 http://dx.doi.org/10.1007/s00222-008-0126-x | Zbl 1145.53055

[5] Apostolov V., Tønnesen-Friedman C., A remark on Kähler metrics of constant scalar curvature on ruled complex surfaces, Bull. London Math. Soc., 2006, 38(3), 494–500 http://dx.doi.org/10.1112/S0024609306018480 | Zbl 1122.53042

[6] Besse A.L., Einstein Manifolds, Ergeb. Math. Grenzgeb., 10, Springer, Berlin, 1987

[7] Donaldson S.K., Symmetric spaces, Kähler geometry and Hamiltonian dynamics, In: Northern California Symplectic Geometry Seminar, Amer. Math. Soc. Transl. Ser. 2, 196, American Mathematical Society, Providence, 1999, 13–33 | Zbl 0972.53025

[8] Donaldson S.K., Kronheimer P.B., The Geometry of Four-Manifolds, Oxford Math. Monogr., Clarendon Press/Oxford University Press, New York, 1990 | Zbl 0820.57002

[9] Fujiki A., Remarks on extremal Kähler metrics on ruled manifolds, Nagoya Math. J., 1992, 126, 89–101 | Zbl 0772.53044

[10] Garcia-Fernandez M., Coupled Equations for Kähler Metrics and Yang-Mills Connections, PhD thesis, Universidad Autónoma de Madrid, Madrid, 2009, preprint available at http://arxiv.org/abs/1102.0985

[11] Guan D., Existence of extremal metrics on compact almost homogeneous Kähler manifolds with two ends, Trans. Amer. Math. Soc., 1995, 347(6), 2255–2262 | Zbl 0853.53047

[12] Guan D., On modified Mabuchi functional and Mabuchi moduli space of Kähler metrics on toric bundles, Math. Res. Lett., 1999, 6(5–6), 547–555 | Zbl 0968.53050

[13] Guan D., Existence of extremal metrics on almost homogeneous manifolds of cohomogeneity one. III, Internat. J. Math., 2003, 14(3), 259–287 http://dx.doi.org/10.1142/S0129167X03001806 | Zbl 1048.32014

[14] Koiso N., Sakane Y., Nonhomogeneous Kähler-Einstein metrics on compact complex manifolds, In: Curvature and Topology of Riemannian Manifolds, Katata, August 26–31, 1985, Lecture Notes in Math., 1201, Springer, Berlin, 1986, 165–179 http://dx.doi.org/10.1007/BFb0075654

[15] Tønnesen-Friedman C.W., Extremal Kähler metrics on minimal ruled surfaces, J. Reine Angew. Math., 1998, 502, 175–197 http://dx.doi.org/10.1515/crll.1998.086 | Zbl 0921.53033