Forms and currents defining generalized p-Kähler structures



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.


Kähler manifold Balanced manifold SKT manifold SG manifold p-Kähler manifold Positive forms and currents 

Mathematics Subject Classification

Primary 53C55 Secondary 53C56 32J27 


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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Dipartimento di Scienze Matematiche Fisiche e InformaticheUniversità di ParmaParmaItaly

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