International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 3, Pages 545-556
doi:10.1155/S0161171293000675

Real hypersurfaces of indefinite Kähler 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.