Semi-stable holomorphic vector bundles over generalized Kähler manifolds

ABSTRACT

In this paper, by using Uhlenbeck–Yau's continuity method, we prove the existence of approximate Hermite–Einstein structure on the semi-stable generalized holomorphic bundles over closed generalized Kähler manifolds of symplectic type.

Keywords:

• Generalized holomorphic bundle
• generalized Kähler manifold
• semi-stability
• approximate Hermite–Einstein structure
• pure spinor

AMS SUBJECT CLASSIFICATIONS:

• 53C07
• 53C55

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The author is supported by the Natural Science Foundation of Universities of Anhui Province [grant number K120431039] and the Fundamental Research Funds for the Central Universities [grant number 19lgpy239]. The author is partially supported by National Natural Science Foundation of China [grant numbers 11625106, 11801535, 11721101]. The research is partially supported by the project “Analysis and Geometry on Bundle” of Ministry of Science and Technology of the People's Republic of China [grant number SQ2020YFA070080].