A note about almost contact metric hypersurfaces axioms for almost Hermitian manifolds

Abstract

From 1950s, it is known that an almost contact metric structure is in­duced on an arbitrary oriented hypersurface in an almost Hermitian mani­fold. In accordance with the definition, an almost Hermitian manifold satisfies the axiom of almost contact hypersurfaces endowed with a some property, if an almost contact hypersurface with this property passes through every point of considered almost Hermitian manifold. In the present note, we discuss some problems related to almost con­tact metric hypersurfaces axioms for almost Hermitian manifolds. In par­ticular, we select some special types of almost contact metric hypersur­faces axioms for almost Hermitian manifolds. We mark out the axioms consisting of the conditions for the almost contact metric structure on the hypersurface of an almost Hermitian manifold to belong to a special class (for example, to the class of Sasakian or quasi-Sasakian structures). We also mark out the axioms that are related to the second fundamental form of the immersion of the almost contact metric hypersurface into an almost Hermitian manifold.

Keywords

• almost contact metric structure
• almost hermitian mani­fold
• almost contact metric hypersurfaces axioms
• oriented hypersurface