3 citations · 10 across the 17 of their papers we have counts for
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Hermitian threefolds with constant holomorphic sectional curvature
Shuwen Chen, Fangyang Zheng
An old conjecture in non-Kähler geometry states that if the Chern holomorphic sectional curvature of a compact Hermitian manifold is equal to a constant , then the metric must b…
Hermitian connections with parallel torsion and constant holomorphic sectional curvature
Shuwen Chen, Fangyang Zheng
A long-standing conjecture in non-Kähler geometry states that a compact Hermitian manifold with constant Chern holomorphic sectional curvature should be Kähler when the constant is…
Hermitian Connections with Parallel Torsion and the Fino--Vezzoni Conjecture
Shuwen Chen, Fangyang Zheng
We prove that the Fino--Vezzoni conjecture holds on every compact complex manifold carrying a Hermitian connection with parallel torsion. More precisely, if a compact connected com…
The Fino-Vezzoni conjecture on balanced Bismut torsion-parallel manifolds
Shuwen Chen, Fangyang Zheng
We study the Fino-Vezzoni conjecture on compact complex manifolds carrying a balanced Bismut torsion-parallel Hermitian metric. We prove that if such a manifold also admits a pluri…
Curvature property on Hermitian Lie algebras with abelian ideals of codimension two
Shuwen Chen, Fangyang Zheng
Let be a unimodular Hermitian Lie algebra containing an abelian ideal of real codimension two. We study the curvature behaviour of and show th…
Locally conformally Kähler manifolds with constant Levi-Civita or Bismut holomorphic sectional curvature
Shuwen Chen, Fangyang Zheng
AAn old conjecture in non-Kähler geometry states that any compact Hermitian manifold with constant Chern holomorphic sectional curvature must be either Kähler or Chern flat. The co…