Author

Shu-Wen Chen

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Preprint Sep 2026

Hermitian threefolds with constant holomorphic sectional curvature

An old conjecture in non-K\"ahler geometry states that if the Chern holomorphic sectional curvature of a compact Hermitian manifold is equal to a constant $c$, then the metric must be K\"ahler when $c\neq 0$ and be Chern flat when $c=0$. The conjecture is known to be true in dimension two by the work of Balas--Gauducho...

Shu-Wen Chen, Fang-Yang Zheng · 0 citations

Preprint Sep 2026

Hermitian connections with parallel torsion and constant holomorphic sectional curvature

A long-standing conjecture in non-K\"ahler geometry states that a compact Hermitian manifold with constant Chern holomorphic sectional curvature should be K\"ahler when the constant is nonzero and Chern flat when the constant is zero. In this article, we study the corresponding problem for a Hermitian connection $\nabl...

Shu-Wen Chen, Fang-Yang Zheng · 1 citation

Preprint Aug 2026

Curvature property on Hermitian Lie algebras with abelian ideals of codimension two

Let $(\mathfrak g,J,g)$ be a unimodular Hermitian Lie algebra containing an abelian ideal $\mathfrak a$ of real codimension two. We study the curvature behaviour of $g$ and show that, if $g$ has constant Chern holomorphic sectional curvature, then it must be Chern flat. We also show that, for every canonical metric con...

Shu-Wen Chen, Fang-Yang Zheng · 1 citation