5 problems

Let $X$ be a compact locally conformally Kähler (lcK) manifold, and let $h^{1,2}(X)$ denote its Dolbeault number. A Hermitian metric is pluriclosed if its fundamental form is $^c$-…

Let ${\mathfrak g}$ be a nilpotent Lie algebra with a complex structure, and suppose that ${\mathfrak g}$ admits a pluriclosed inner product. Pluriclosed two-step nilpotency conjec…

Let $(M^n,g)$ be a compact Hermitian manifold, and let the Strominger connection be the metric connection associated with the Hermitian structure. The connection is Kähler-like if…

Let $M$ be a compact complex manifold. A Hermitian metric is balanced if its fundamental form $\omega$ satisfies $d(\omega^{n-1})=0$, and it is pluriclosed if $dd^c\omega=0$. The b…

Let $M$ be a compact complex manifold endowed with a Hermitian metric, and let its Strominger–Bismut connection be the Hermitian connection associated with that metric. The Stromin…