This paper is devoted, first of all, to give a complete unified proof of the characterization theorem for compact generalized Kähler manifolds. The proof is based on the classical duality between “closed” positive forms and “exact” positive currents. In the last part of the paper we approach the general case of non compact complex manifolds, where “exact” positive forms seem to play a more significant role than “closed” forms. In this setting, we state the appropriate characterization theorems and give some interesting applications.

中文翻译：

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定义广义 p-Kähler 结构的形式和潮流

本文首先致力于给出紧广义 Kähler 流形的表征定理的完整统一证明。该证明基于“闭合”正形式和“精确”正电流之间的经典二元性。在论文的最后一部分，我们讨论了非紧复杂流形的一般情况，其中“精确”正形式似乎比“封闭”形式发挥更重要的作用。在这种情况下，我们陈述了适当的表征定理并给出了一些有趣的应用。