an:04086452
Zbl 0664.53011
Li, Jun; Yau, Shing Tung
Hermitian-Yang-Mills connection on non-K??hler manifolds
EN
Mathematical aspects of string theory, Proc. Conf., San Diego/Calif. 1986, Adv. Ser. Math. Phys. 1, 560-573 (1987).
1987
a
53C05 32L05 35Q99 81T08
Hermitian-Yang-Mills connections; stable holomorphic bundles; non- K??hler Hermitian complex manifolds; instantons; string theory
[For the entire collection see Zbl 0651.00012.]
The theorem of Donaldson and Uhlenbeck-Yau relating Hermitian-Yang-Mills connections to stable holomorphic bundles [S. K. Donaldson, Duke Math. J. 54, 231-247 (1987; Zbl 0627.53052); \textit{K. Uhlenbeck} and \textit{S. T. Yau}, Commun. Pure. Appl. Math. 39, S 257-S 293 (1986; Zbl 0615.58045)] is suspectible to generalizations in various directions. One needs on the one hand a gauge-theoretic differential equation of Yang-Mills type and on the other an algebro-geometric notion of stability. In this paper, the authors refine their original method to cover the case of non-K??hler Hermitian complex manifolds. The 2-dimensional case of this result, proved by a ``direct'' method was in fact done independently by \textit{N. P. Buchdahl} [Math. Ann. 280, 625-648 (1988; Zbl 0617.32044)] and has already been used by Braam and Hurtubise to study instantons on Hopf surfaces. The authors have in mind a motivation arising from the demands of physicists studying string theory.
N.Hitchin
Zbl 0637.32023; Zbl 0651.00012; Zbl 0627.53052; Zbl 0615.58045; Zbl 0617.32044