Abstract: It
is known that a 4-dimensional oriented pseudo-Riemannian
manifold M
with a neutral metric admits
two kinds of almost complex structures J,
with
different orientations. Of course, M
admits a Riemannian metric g.
For such a 4-manifold M,
there exists a quadruple such
that g and
are
both invariant by both J
and Then
the purpose of the present paper is to analyze the
relations between almost Hermitian structures (g,
J),in a
Riemannian structure and almost neutral Hermitian
structures in an
indefinite structure. Our analysis developed here is
based on the author’s previous papers [JP J. Geom.
Top. 5(2) (2005), 155-176], [JP J. Geom. Top. 5(3)
(2005), 251-274].
Keywords and phrases: almost complex structure, opposite almost complex structure, almost Hermitian structure, opposite almost Hermitian structure, almost Kähler structure, opposite almost Kähler structure, Kähler structure, opposite Kähler structure.
