On Strominger space forms

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 Kähler. The main result of this article is to confirm the conjecture in dimension $2$. We also verify the conjecture in higher dimensions in a couple of special situations.

arXiv commentAdded 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