Real hypersurfaces of indefinite Kaehler manifolds

A. Bejancu,K. L. Duggal

doi:10.1155/s0161171293000675

A. Bejancu, K. L. Duggal

Open Access

https://doi.org/10.1155/s0161171293000675

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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 pseudosphereS2S2n+1(1) or of the pseudohyperbolic spaceH2S−12n+1(1). Finally, we get the causal character of ( ϵ ) cosymplectic real hypersurfaccs of indefinite complex space-forms.

Highlights

Indefinite Kahler manifolds have been introduced by Barros-R.(,mcr [1]
In the first section we introduce (e)-Sasakian manifolds which enclose the class of usual Sasakian manifolds
It has to be noted that in the definition of an (e)-Sasakian manifold it is essential that the causal character of the characteristic vector field of the structure is preserved

Summary

Introduction

Indefinite Kahler manifolds have been introduced by Barros-R.(,mcr [1]. Because of the signature of the metric we expect some essential changes in the study of submanifolds in such spaces. M is called a space-like almost contact metric manifold. For an (e)-almost contact metric manifold M, the following are equivalent- Sasakian manifolds with indefinite metrics have been first considered by Takahashi [9].

Results

Conclusion