The Kobayashi–Hitchin Correspondence of Generalized Holomorphic Vector Bundles Over Generalized Kähler Manifolds of Symplectic Type

Abstract In this paper, we establish the Kobayashi–Hitchin correspondence, that is, equivalence of existence an Einstein–Hermitian metric and $\psi $-polystability a generalized holomorphic vector bundle over compact Kähler manifold symplectic type. Poisson modules provide intriguing bundles, obtain $-stable complex surfaces are not stable in ordinary sense.