On nearly Kählerian manifolds and quasi-Sasakian hypersurfaces axiom

Abstract

It is known that an almost contact metric structure is induced on an arbitrary hypersurface of an almost Hermitian manifold. The case when the almost Hermitian manifold is nearly Kählerian and the almost contact metric structure on its hypersurface is quasi-Sasakian is considered. It is proved that non-Kählerian nearly Kählerian manifolds (in particular, the six-dimensional sphere equipped with the canonical nearly Kählerian structure) do not satisfy to the quasi-Sasakian hypersurfaces axiom.

Keywords

• almost hermitian manifold
• nearly kählerian manifold
• almost contact metric structure
• quasi-sasakian hypersurfaces axiom