Narasimhan-Seshadri connection and Kähler structure of the space of moduli of holomorphic vector bundles over Riemann surfaces
Let \(N=N(n,0)\) be the moduli space of stable vector bundles of rank n and degree 0 over compact Riemann surface S of genus \(g>1\), \(\omega\) is closed (1,1)-form, defining natural Kähler structure on N, and \(A_ E\)- Narasimhan-Seshadri connection, the unique flat unitary connection on a stable vector bundle E of degree 0 over S, compatible with complex structure. The authors show that \(A_ E\) plays in relation to \(\omega\) the same role, as Fuchsian projective connection on S with respect to Weil-Petersson simplectic form on Teichmüller space T(S) [see the authors' paper in Funct. Anal. Appl. 19, 219-220 (1985); translation from Funkts. Appl. Prilozh. 19, No.3, 67-68 (1985; Zbl 0612.31018)], namely, \({\bar \partial}A_ E=-2\sqrt{-1}\omega.\)
scientific article; zbMATH DE number 3993974