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.
Funder
Simons Foundation
Università degli Studi di Torino
Publisher
Springer Science and Business Media LLC
Reference23 articles.
1. Alessandrini, L.: $$p$$-Kähler Lie groups. Arch. Math. (Basel) 61(6), 549–559 (1993)
2. Alessandrini, L., Andreatta, M.: Closed transverse $$(p, p)$$-forms on compact complex manifolds. Compos. Math. 61(2), 181–200 (1987)
3. Alessandrini, L., Andreatta, M.: Erratum: closed transverse $$(p, p)$$-forms on compact complex manifolds. Compos. Math. 63(3), 143 (1987)
4. Alessandrini, L., Bassanelli, G.: Compact $$p$$-Kähler manifolds. Geom. Dedicata. 38(2), 199–210 (1991)
5. Alessandrini, L., Bassanelli, G.: Positive $$\partial {\bar{\partial }}$$-closed currents and non-Kähler geometry. J. Geom. Anal. 2, 291–316 (1992)