On Fubinian and C-Fubinian manifolds

In his previous papers^, one of the present authors proved that an orientable hypersurface in an almost complex manifold has an almost contact structure and obtained a condition 2) in order that a hypersurface in a Kahlerian manifold is Sasakian. In the present paper, a hypersurface satisfying the condition will be called a C-umbilical hypersurface. A manifold having the same Sasakian structure as a C-umbilical hypersurface in a locally Fubinian manifold will be said to be locally C-Fubinian. The purpose of the present paper is to show some characteristic properties of Fubinian and C-Fubinian manifolds.