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math.DG2025
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 $…
math.DG2025
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…