On Strominger space forms

TL;DR

This paper investigates a conjecture relating the Strominger connection's curvature to the Kähler property of Hermitian manifolds, confirming it in dimension two and in special cases for higher dimensions.

Contribution

It proves the conjecture for compact Hermitian surfaces and verifies it in specific higher-dimensional cases, advancing understanding of Strominger space forms.

Findings

Confirmed the conjecture in dimension 2

Verified the conjecture in special higher-dimensional cases

Connected constant non-zero holomorphic sectional curvature to Kähler metrics

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 $2$. We also verify the conjecture in higher dimensions in a couple of special situations.