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 . We also verify the conjecture in higher dimensions in a couple of special situations.
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