10 papers
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…
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…
Curvature characterization of Hermitian manifolds with Bismut parallel torsion
Quanting Zhao, Fangyang Zheng
In this article, we study Hermitian manifolds whose Bismut connection has parallel torsion, which will be called {\em Bismut torsion parallel manifolds,} or {\em BTP} manifolds for…
Bismut torsion parallel metrics with constant holomorphic sectional curvature
Shuwen Chen, Fangyang Zheng
An old conjecture in non-Kähler geometry states that, if a compact Hermitian manifold has constant holomorphic sectional curvature, then the metric must be Kähler (when the const…
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…
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…