A note on p-Kähler structures on compact quotients of Lie groups

Abstract A p -Kähler structure on a complex manifold of complex dimension n is given by a d -closed transverse real (p, p) -form. In the paper, we study the existence of p -Kähler structures on compact quotients of simply connected Lie groups by discrete subgroups endowed with an invariant complex structure. In particular, we discuss the existence of p -Kähler structures on nilmanifolds, with a focus on the case p =2 p = 2 and complex dimension n = 4 n = 4. Moreover, we prove that a (n-2) (n - 2) -Kähler almost abelian solvmanifold of complex dimension n 3 n ≥ 3 has to be Kähler.