7 papers
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…
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…
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 const…
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 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…
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…