3 problems

Let $(M^{n},g)$ be a compact Hermitian manifold with $n\geq2$. For a $(1,0)$-vector $X$, let $\mathcal{C}_{\alpha,\beta}(X)$ denote the mixed curvature, formed from the relevant Ch…

Let $(M^{n},g)$ be a compact Hermitian manifold with $n\geq2$. For $k\in\{1,2,3,4\}$ and $\beta\neq0$, define the kth-mixed curvature by … where $Ric^{(k)}$ is the kth Chern Ricci…

Let $(M^{n},g)$ be a compact Hermitian manifold with $n\geq2$. The holomorphic sectional curvature is $H(X)=R(X,\overline{X},X,\overline{X})/|X|^{4}$ for nonzero $(1,0)$-vectors…