On $\zeta$-Normalized Null Hypersurfaces of Indefinite Sasakian Manifolds

Year 2025, Volume: 18 Issue: 2, 170 - 184, 19.10.2025

Theophile Kemajou Mbiakop

https://doi.org/10.36890/iejg.1611755

Abstract

We examine null hypersurfaces that are normalized by the structure vector field $\zeta$ (briefly, $\zeta$-normalized null hypersurfaces) in almost contact metric manifolds. We characterize the geometry of such null hypersurfaces, and an example is provided. We show that leaves of an integrable screen distribution within these hypersurfaces admit an almost contact metric structure $(\psi,h,\nu,U,)$. In cases where the ambient space is an indefinite Sasakian, we show that it is not always possible to choose a structure vector field with specific geometric properties, along with prescribed geometric properties for the null hypersurface. The necessary and sufficient condition for normality of $(\psi,h,\nu,U,)$-structure is established. Integrability conditions for the distributions on a $\zeta$-normalized null hypersurface of an indefinite Sasakian manifolds are investigated.

Keywords

$\zeta$- null hypersurface , rigging vector field , almost contact manifold , indefinite sasakian manifolds

Thanks

The authors thank the anonymous referees for their useful comments and their helpful suggestions that will improve the quality of this paper.

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