Year: 2026
Type: preprint
Abstract: We regard the Chern torsion of a Hermitian manifold as a skew-symmetric complex-bilinear product on its holomorphic tangent bundle. For a compact connected Chern--Kähler-like Hermitian manifold, we prove that this product satisfies the Jacobi identity pointwise. If, in addition, the Chern holomorphic sectional curvature is strongly quasi-positive, we show that the resulting torsion Lie algebra is nilpotent and must be abelian. Consequently, the metric is Kähler. The underlying complex manifold is therefore projective and rationally connected. For general Hermitian manifolds, we construct a metric with positive real bisectional curvature on a Hopf surface which is neither simply connected nor rationally connected.
Source: arXiv (Cornell University)
Authors: Lin, Wangyang, Ren, Yibo
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204940681