Abstract.Small deformations of Kahler manifolds are Kahler too; we prove here that this is not true for balanced manifolds nor, more generally,

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Some extension problems are considered here for the class of plurisubharmonic currents, i.e. real currents T such that idfiT is positive. In particular we prove the following theorem: "Let Ω be an open subset of C N and Fan analytic subset of Ω. Suppose Tis a negative plurisubharmonic current on Ω -Υ of bidimension (p,p)\ if dim Y

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In this paper we study compact complex non-K/ihler manifolds, in particular the holomorphically parallelizable ones, by means of their degree of p-K/ihlerianity, which can also be characterized by the absence of a certain class of holomorphic k-forms or of a certain class of currents on the manifold. We give several examples to emphasize the structure and the behaviour of this kind of non-K/ihler manifolds.