5 papers · 1 filter
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…
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…
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…