11 papers
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…
A survey of The Prouhet-Tarry-Escott Problem and its Generalizations
Chen Shuwen
This paper explores the Prouhet-Tarry-Escott problem (PTE), the Generalized PTE problem (GPTE), and the Fermat form of Generalized PTE problem (FPTE). The GPTE problem extends the…
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…
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…
On Strominger space forms
Shuwen Chen, Fangyang Zheng
In this article, we propose the following conjecture: if the Strominger connection of a compact Hermitian manifold has constant non-zero holomorphic sectional curvature, then the H…