Chern number identities on compact complex surfaces and applications
Differential Geometry
2025-08-18 v1
Abstract
In this paper, we establish Chern number identities on compact complex surfaces. As an application, we prove that if is a compact Riemannian four-manifold with constant scalar curvature and admits a compatible complex structure such that the complexified Ricci curvature is a non-positive form, then is a K\"ahler surface.
Cite
@article{arxiv.2508.11171,
title = {Chern number identities on compact complex surfaces and applications},
author = {Xiaokui Yang},
journal= {arXiv preprint arXiv:2508.11171},
year = {2025}
}