3 citations · 10 across the 17 of their papers we have counts for
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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…
Hermitian connections with parallel torsion and constant holomorphic sectional curvature
Shuwen Chen, Fangyang Zheng
A long-standing conjecture in non-Kähler geometry states that a compact Hermitian manifold with constant Chern holomorphic sectional curvature should be Kähler when the constant is…
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 $…
A note on almost abelian groups with constant holomorphic sectional curvature
Yulu Li, Fangyang Zheng
A long-standing conjecture in non-Kähler geometry states that if the Chern (or Levi-Civita) holomorphic sectional curvature of a compact Hermitian manifold is a constant , then…
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…
On solvmanifolds with complex commutator and constant holomorphic sectional curvature
Xin Huang, Fangyang Zheng
An old open question in non-Kähler geometry predicts that any compact Hermitian manifold with constant holomorphic sectional curvature must be Kähler or Chern flat. The conjecture…
Chern flat manifolds that are torsion-critical
Dongmei Zhang, Fangyang Zheng
In our previous work, we introduced a special type of Hermitian metrics called {\em torsion-critical,} which are non-Kähler critical points of the -norm of Chern torsion over…
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…
Streets-Tian Conjecture on several special types of Hermitian manifolds
Yuqin Guo, 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…
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 constan…
A note on compact homogeneous manifolds with Bismut parallel torsion
Fabio Podestà, Fangyang Zheng
In this article, we investigate the class of Hermitian manifolds whose Bismut connection has parallel torsion ({\rm BTP} for brevity). In particular, we focus on the case where the…
A classification of locally Chern homogeneous Hermitian manifolds
Lei Ni, Fangyang Zheng
We apply the algebraic consideration of holonomy systems to study Hermitian manifolds whose Chern connection is Ambrose-Singer and prove structure theorems for such manifolds. The…
Kähler manifolds and cross quadratic bisectional curvature
Lei Ni, Fangyang Zheng
In this article we continue the study of the two curvature notions for Kähler manifolds introduced by the first named author earlier: the so-called cross quadratic bisectional curv…
On compact Hermitian manifolds with flat Gauduchon connections
Bo Yang, Fangyang Zheng
Given a Hermitian manifold , the Gauduchon connections are the one parameter family of Hermitian connections joining the Chern connection and the Bismut connection. We wil…