Anti-abelian nearly Kähler structures on nilpotent Lie algebras

Morozov (Izv Vyss Ucebn Zaved Mat 4(5):161–171, 1958), classified six-dimensional nilpotent Lie algebras (see also Di Scala and Vezzoni in Ann Global Anal Geom 40:21–45, 2011 for more details). In this paper, we classify anti-abelian almost product structures for these Lie algebras. Then we determine anti-abelian almost para-complex structures on 6-dimensional nilpotent Lie algebras. Finally, it is shown that only one of them admits nearly para-Kähler structures.