Abstract: On the basis of a recent paper I-N [5] (General
procedure - neutral version -) of a series of papers, we study two kinds of
almost neutral Hermitian structures on a nilpotent Lie group (a nilmanifold). It is shown that admits two kinds of almost neutral
Kähler structures (double neutral almost Kähler structures), which cannot be
double neutral Kähler. Moreover, admits a double isotropic Kähler
structure.
Keywords and phrases: nilpotent Lie group, nilmanifold, geometric structures on
4-manifolds, almost neutral Kähler structure, opposite almost neutral Kähler structure, isotropic Kähler structure.