We show the existence of ( ϵ )-almost contact metric structures and give examples
of ( ϵ )-Sasakian manifolds. Then we get a classification theorem for real hypersurfaces of
indefinite complex space-forms with parallel structure vector field. We prove that ( ϵ )-Sasakian
real hypersurfaces of a semi-Euclidean space are either open sets of the pseudosphere
S2S2n+1
(1) or of the pseudohyperbolic space H2S−12n+1(1). Finally, we get the causal character of ( ϵ )
cosymplectic real hypersurfaccs of indefinite complex space-forms.