Certain almost contact hypersurfaces in Euclidean spaces.

An odd-dimensional differentiate manifold M is said to have an almost contact structure or to be an almost contact manifold if the structural group of its tangent bundle is reducible to the product of a unitary group with the 1-dimensional identity group [3]. Recently Sasaki and Hatakeyama [4, 5] proved that an almost contact structure is equivalent to the existence of a set of tensor fields φ, ξ, -η of the type (1, 1), (1, 0) and (0, 1) satisfying the following five conditions: