3 citations · 4 across the 15 of their papers we have counts for
18 papers
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…
Flat Hermitian Lie algebras are Kähler
Dongmei Zhang, Fangyang Zheng
In 1976, Milnor classified all Lie groups admitting a flat left-invariant metric. They form a special type of unimodular 2-step solvable groups. Considering Lie groups with Hermiti…
On Hermitian manifolds with constant mixed curvature
Shuwen Chen, Fangyang Zheng
In a recent work, Kai Tang conjectured that any compact Hermitian manifold with non-zero constant mixed curvature must be Kähler. He confirmed the conjecture in complex dimension $…