The authors define p-Kähler manifolds requiring the existence of closed (p,p)-forms transverse to the complex structure and then characterize them by a condition on the space of positive currents of the manifolds. The behaviour of the p-Kähler condition with respect to holomorphic submersions and immersions is also studied. Some examples of p-Kähler manifolds are invalid due to the failure of Lemma 2.3 [cf. the erratum].
Closed transverse (p,p)-forms on compact complex manifolds / L. Alessandrini; M. Andreatta. - In: COMPOSITIO MATHEMATICA. - ISSN 0010-437X. - 61(1987), pp. 181-200.
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