Totally geodesic hypersurfaces of Kaehler manifolds

It is known that a C°° orientable totally umbilical hypersurface P with nonzero mean curvature of a Eaehler manifold M is a normal contact manifold.Moreover, if M = C n 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.