Non-Hermitian Yang-Mills connections

Selecta Mathematica, New Series

Volumn 4, Issue 2, 1998, Pages 279-320

  Kaledin, D ^a   Verbitsky, M ^b  

^a INSTITUT DES HAUTES ÉTUDES SCIENTIFIQUES   (France)

^b INDEPENDENT UNIVERSITY OF MOSCOW   (Russian Federation)

Author keywords

Hyperk hler; Twistor; Yang mills

Indexed keywords

EID: 54749107608     PISSN: 10221824     EISSN: 14209020     Source Type: Journal    
DOI: 10.1007/s000290050033     Document Type: Article

References (18)

1. [C] E. Calabi. Metriques kähleriennes et fibres holomorphes. Ann. Ecol. Norm. Sup. 12 (1979), 269-294.
2. [Don] S. K. Donaldson. Anti-self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles. Proc. London Math. Soc. 50 (1985), 1-26.
3. [H] N. J. Hitchin. The self-duality equations on a Riemann surface. Proc. London Math. Soc. (3) 55 (1987), 59-126.
4. [HKLR] N. J. Hitchin, A. Karlhede, U. Lindström and M. Roček. Hyperkähler metrics and supersymmetry. Comm. Math. Phys. 108 (1987), 535-589.
5. [Kob] S. Kobayashi. Differential geometry of complex vector bundles. Princeton University Press, 1987.
6. [LY] Jun Li and S.-T. Yau. Hermitian Yang-Mills connections on non-Kähler manifolds. In: mathematical aspects of string theory (S.T. Yau, ed.). World Scientific Publ., London, 1987, pp. 560-573.
7. [Lü] M. Lübcke. Chernklasses von Hermite-Einstein Vektorbündeln. Math. Ann. 260 (1982), 133-141.
8. [Mu] S. Mukai. Symplectic structure of the moduli space of sheaves on abelian or K3 surfaces. Invent. Math. 77 (1984), 101-116.
9. [Sal] S. Salamon. Quaternionic Kahler manifolds. Inv. Math. 67 (1982), 143-171.
10. [Sim1] C.T. Simpson. Constructing variations of Hodge structure using Yang-Mills theory, and applications to uniformization. Jour, of Amer. Math. Soc. 4 (1988), 867-918.
11. [Sim2] C.T. Simpson. Moduli of representations of the fundamental group of a smooth projective variety, I. Publ. Math. IHES 79 (1994), 47-129;
12. C.T. Simpson. Moduli of representations of the fundamental group of a smooth projective variety, II. Publ. Math. IHES 80 (1994), 5-79.
13. [Sim3] C.T. Simpson. Higgs bundles and local systems. Publ. Math. IHES 75 (1992), 5-95.
14. [UY] K. Uhlenbeck and S.-T. Yau. On the existence of Hermitian Yang-Mills connections in stable vector bundles. Comm. in Pure and Appl. Math. 39 (1986), S257-S293.
15. [V-bun] M. Verbitsky. Hyperholomorphic bundles over a hyperkähler manifold, alg-geom electronic preprint 9307008, 43 p. also published in: Journ. of Alg. Geom. 5 (1996), 633-669.
16. [V-so5] M. Verbitsky. On the action of the Lie algebra so(5) on the cohomology of a hyperkähler manifold. Func. Anal. and Appl. 24 (1990), 70-71.
17. [V-sym] M. Verbitsky. Hyperkähler embeddings and holomorphic symplectic geometry II. alggeom electronic preprint 9403006, 14 p.,
18. also published in: GAFA 5 (1995), 92-104.