Null hypersurface normalized by the structure vector field in a para-Sasakian manifold

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Keywords:

Almost paracontact manifold, Para-Sasakian manifold, K-Normalized null hypersurface, Rigging vector field, Structure vector field

Abstract

 We examine the geometry of a null hypersurface $M$ of a para-Sasakian manifold $(\overline{M},\overline{\phi}, K, \overline{\eta},\overline{g})$ transversal to the structure vector field $K$. The {later} is then a rigging $\zeta$ for $M$, and $M$ is called $K$-normalized null hypersurface. We characterize the geometry of such a null hypersurface and prove under some conditions that there exist leaves of an integrable distribution of the screen distribution admitting an almost para complex structure. Also, we derive certain non-existence results and discuss some properties of semi-symmetric(resp. locally symmetric) $K$-normalized null hypersurfaces of para-Sasakian manifolds, for instance, we demonstrate that any para-Sasakian manifold admitting a semi-symmetric totally geodesic $K$-normalized null hypersurface is of constant negative curvature along the null hypersurface.

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Published

2025-03-23

How to Cite

Kemajou Mbiakop, T., & Ngakeu, F. . (2025). Null hypersurface normalized by the structure vector field in a para-Sasakian manifold. International Journal of Maps in Mathematics, 8(1), 85–105. Retrieved from https://simadp.com/journalmim/article/view/217