Writing long books is a laborious and impoverishing act of foolishness: expanding in five
hundred pages an idea that could be perfectly explained in a few minutes. A better …

An LCK manifold is a complex manifold (M,I) equipped with a Hermitian form ω and a closed
1-form θ, called the Lee form, such that dω=θ∧ω. An LCK manifold with potential is an LCK …

The goal of this note is to give an introduction to locally conformally symplectic and Kähler
geometry. In particular, the first two sections aim to provide the reader with enough …

We prove that a compact lcK manifold with holomorphic Lee vector field is Vaisman provided
that either the Lee field has constant norm or the metric is Gauduchon (ie, the Lee field is …

Oeljeklaus–Toma (OT) manifolds are complex non-Kähler manifolds whose construction
arises from specific number fields. In this note, we compute their de Rham cohomology in …

Vaisman's theorem for locally conformally K\" ahler (lcK) compact manifolds states that any
lcK metric on a compact complex manifold which admits a K\" ahler metric is, in fact, globally …

We prove that the deRham cohomology classes of Lee forms of locally conformally
symplectic structures taming the complex structure of a compact complex surface $ S $ with …

We obtain structure results for locally conformally symplectic Lie algebras. We classify
locally conformally symplectic structures on four-dimensional Lie algebras and construct …

We investigate the relation between holomorphic torus actions on complex manifolds of
locally conformally Kähler (LCK) type and the existence of special LCK metrics. We show …

Let M be a complex manifold and L an oriented real line bundle on M equipped with a flat
connection. A “locally conformally Kähler”(LCK) form is a closed, positive (1, 1)-form taking …