Hermitian variation of an almost pseudo-Kähler metric
Volume 136 / 2026
Annales Polonici Mathematici 136 (2026), 33-51
MSC: Primary 53C55; Secondary 53B12
DOI: 10.4064/ap241018-24-6
Published online: 20 November 2025
Abstract
Given an almost pseudo-Kähler manifold and a vector field we construct an almost pseudo-Hermitian metric. We study under which conditions this new pseudo-Hermitian metric is also almost pseudo-Kähler and we use it to get some information about holomorphic vector fields on a compact pseudo-Kähler manifold with index 2. We also study the relationship between holomorphic statistical structures and the newly constructed pseudo-Hermitian metric.
