It is known that a C∞
orientable totally umbilical hypersurface P with nonzero mean curvature of a Kaehler
manifold M is a normal contact manifold. Moreover, if M = Cn with the flat Kaehler
metric, P can be realized as a normal contact metric manifold of positive constant
curvature. It is the main purpose of this paper to obtain corresponding results for
cosymplectic manifolds.
The direct product of two normal almost contact manifolds can be endowed with
a complex structure. For cosymplectic manifolds more is obtained. Indeed, the direct
product of two cosymplectic manifolds can be given a Kaehlerian structure. This is
particularly true of orientable totally geodesic hypersurfaces of a Kaehler
manifold.
