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

Abstract

AbstractA 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 $$n\ge 3$$ n ≥ 3 has to be Kähler.