7 papers · 1 filter
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…
Compact balanced threefolds and LCK manifolds with constant holomorphic sectional curvature
Shuwen Chen, Junpeng Li
A long-standing conjecture in Hermitian geometry says that a compact Hermitian manifold with constant Chern holomorphic sectional curvature is Kähler for and Chern fl…
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 $…
Canonical metric connections with constant holomorphic sectional curvature
Shuwen Chen, Fangyang Zheng
We consider the conjecture of Chen and Nie concerning the space forms for canonical metric connections of compact Hermitian manifolds. We verify the conjecture for two special type…
Streets-Tian Conjecture holds for 2-step solvmanifolds
Shuwen Chen, Fangyang Zheng
A Hermitian-symplectic metric is a Hermitian metric whose Kähler form is given by the -part of a closed -form. Streets-Tian Conjecture states that a compact complex manif…