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2012 | 10 | 5 | 1673-1687
Tytuł artykułu

Nontrivial examples of coupled equations for Kähler metrics and Yang-Mills connections

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EN
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EN
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.
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Bibliografia
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [8] Donaldson S.K., Kronheimer P.B., The Geometry of Four-Manifolds, Oxford Math. Monogr., Clarendon Press/Oxford University Press, New York, 1990
  • [9] Fujiki A., Remarks on extremal Kähler metrics on ruled manifolds, Nagoya Math. J., 1992, 126, 89–101
  • [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
  • [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
  • [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
  • [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
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0088-5
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