On nilmanifolds with nilpotent or holomorphically parallelizable complex structures, p-Kähler structures are shown to imply (p+1)-Kähler (or balanced) structures, with new deformation obstructions and cohomological criteria.
Alessandrini, Classes of compact non-K¨ ahler manifolds,C
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p-K\"ahler structures on compact complex manifolds
On nilmanifolds with nilpotent or holomorphically parallelizable complex structures, p-Kähler structures are shown to imply (p+1)-Kähler (or balanced) structures, with new deformation obstructions and cohomological criteria.