On hypersurfaces with Kirichenko–Uskorev structure in Kählerian manifolds

Some criteria of minimality of a hypersurfaces of a Kählerian manifold, equipped with an almost contact metric structure of cosymplectic type, are established. It is proved that a minimal hypersurfaces of a Kählerian manifold, equipped with an almost contact metric Kirichenko–Uskorev structure, is totally umbilical if and only it is totally geodesic.