8 papers
Balanced Bismut torsion-parallel manifold with constant holomorphic sectional curvature
Qingsong Wang, Fangyang Zheng
A long-lasting conjecture in non-Kähler geometry says that any compact Hermitian manifold with constant holomorphic sectional curvature must be either Kähler or Chern flat. The con…
Simplicial Volume and Scalar Curvature on Closed Kähler Surfaces
Jie Min, Fangyang Zheng, Bo Zhu
Let be a closed Kähler surface. We prove that every Riemannian metric on with , where , satisfies $$ \lVert M\rVert\leq \frac{27}{…
Balanced Bismut torsion-parallel fourfolds with constant holomorphic sectional curvature
Qingsong Wang, 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 constan…
Constant holomorphic sectional curvature conjecture and Fino-Vezzoni conjecture
Fangyang Zheng
In this short essay, we will survey on two conjectures in non-Kähler geometry: the constant holomorphic sectional curvature conjecture and the Fino-Vezzoni conjecture. We aim at th…
On balanced Hermitian threefolds with parallel Bismut torsion
Quanting Zhao, Fangyang Zheng
We continue our study on Hermitian manifolds that are {\em Bismut torsion parallel,} or {\em BTP} for brevity, which means that the Bismut connection has parallel torsion tensor. F…
Streets-Tian Conjecture on Lie algebras with codimension abelian ideals
Kexiang Cao, 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…