English

On Strominger space forms

Differential Geometry 2023-02-24 v2

Abstract

In this article, we propose the following conjecture: if the Strominger connection of a compact Hermitian manifold has constant non-zero holomorphic sectional curvature, then the Hermitian metric must be K\"ahler. The main result of this article is to confirm the conjecture in dimension 22. We also verify the conjecture in higher dimensions in a couple of special situations.

Keywords

Cite

@article{arxiv.2111.07108,
  title  = {On Strominger space forms},
  author = {Shuwen Chen and Fangyang Zheng},
  journal= {arXiv preprint arXiv:2111.07108},
  year   = {2023}
}

Comments

Added the missing term in formula (32) (the ninth parenthesis on the right hand side), which resulted in changes in formula (33), (34) and (37, and a couple of sentences after (37) to make the argument go through. The paper will appear in Journal of Geometric Analysis