Abstract: A
solvmanifold is
known as one of 4-dimensional geometries in the
sense of Thurston, which do not admit a complex
structure compatible with group of isometries. In
the present paper, as a piece of a series of works
on such geometries, we study almost complex
structures, as chosen naturally. It is shown that an
almost Hermitian structure chosen naturally on is
neither Hermitian nor almost Kähler, and similarly
that an opposite almost Hermitian structure chosen
naturally on is
neither opposite Hermitian nor opposite almost Kähler.
Keywords and phrases: solvable Lie group, solvmanifold, geometric structures on 4-manifolds, almost Kähler structure, opposite almost Kähler structure.
