6 problems

Let $M=\Gamma\backslash G$ be a nilmanifold, where $G$ is a nilpotent Lie group, and let $J$ be a left-invariant complex structure on $M$. Suppose that $M$ admits a locally conform…

Nonexistence conjecture. If $ne5 3$, then $M^n$ does not admit any locally conformal Kähler metric.

Let $M$ be a compact locally conformal Kähler manifold. Say that $M$ satisfies the Kähler topological restrictions when its topology has the restrictions listed for compact Kähler…

Let $M$ be a compact complex surface, meaning a compact complex manifold of complex dimension $2$. A locally conformal Kähler structure is a Hermitian structure whose Kähler form i…

Let $M$ be a compact locally conformal Kähler (lcK) manifold, and call it globally conformal Kähler (gcK) if its lcK metric is globally conformal to a Kähler metric. Della Vedova–O…

A compact manifold $M^{2n}$ with a locally conformal Kähler (lcK) metric has a locally conformal symplectic form whose Lee form is closed; it is globally conformal Kähler (gcK) whe…