Real hypersurfaces of indefinite Kaehler manifolds

Abstract

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.

Keywords

• ( ϵ )-Sasakian manifolds
• real hypersurfaces
• indefinite complex space-forms
• ( ϵ )-cosymplectic real hypersurfaces
• globally hyperbolic space.