4 problems

Chen–Nie conjecture. Let $(M^n,g)$ be a compact Hermitian manifold. Assume that the holomorphic section curvature of $D^r_s$ is a constant $c$. If $c\neq 0$, then $g$ must be Kähle…

Let $(M^n,g)$ be a compact Hermitian manifold. For real numbers $t$ and $s$, let $\nabla^{(t)}=(1-\frac{t}{2})\nabla+\frac{t}{2}\nabla^b$ be the $t$-Gauduchon connection, and defin…

Let $(M^n,g,g')$ be a compact Hermitian manifold with possibly different Hermitian metrics $g$ and $g'$. Let $D^r_s$ be the canonical metric connection associated with $g$, and let…

SKL-to-pluriclosed conjecture. Every compact SKL manifold is pluriclosed, meaning that its Kähler form $\omega$ satisfies