TY - JOUR T1 - On $\zeta$-Normalized Null Hypersurfaces of Indefinite Sasakian Manifolds AU - Kemajou Mbiakop, Theophile PY - 2025 DA - October Y2 - 2025 DO - 10.36890/iejg.1611755 JF - International Electronic Journal of Geometry JO - Int. Electron. J. Geom. PB - Kazım İlarslan WT - DergiPark SN - 1307-5624 SP - 170 EP - 184 VL - 18 IS - 2 LA - en AB - 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. KW - $\zeta$- null hypersurface KW - rigging vector field KW - almost contact manifold KW - indefinite sasakian manifolds CR - Acet, B.E., Yüksel Perkta¸s, S., Kılıç, E.: On Lightlike Geometry of Para-Sasakian Manifolds. The Scientific World Journal. 1, 696231 (2014). https://doi.org/10.1155/2014/696231 CR - Atindogbé, C., Kemajou Mbiakop, T.: Null hypersurfaces in Brinkmann spacetimes. Bulletin of Mathematical Analysis & Applications. 12(3),(2020). CR - Atindogbé, C., Kemajou Mbiakop, T.: Normalized null hypersurfaces in Lorentzian manifolds admitting a conformal vector field. Differential Geometry-Dynamical Systems. 23,1–17 (2021). CR - Duggal, K.L., Bejancu, A.: Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications. Kluwer Academic Publishers. Netherlands (1996). CR - Duggal, K.L., Sahin, B.: Differential Geometry of Lightlike Submanifolds. Birkhauser Verlag AG. Berlin (2010). CR - [Gutierrez, M., Olea, B.: Induced Riemannian structures on null hypersurfaces. Math. Nachr. 289, 1219–1236 (2016). https://doi.org/10.1002/mana.201400355 CR - Kaneyuki, S., Kozai, M.: Paracomplex structures and affine symmetric spaces. Tokyo Journal of Mathematics. 8(1), 81–98(1985). https://doi.org/10.3836/tjm/1270151571 CR - Kemajou Mbiakop, T., Palmas, O.: Screen isotropic leaves and Simons’ formula for null hypersurfaces. Bulletin of the Korean Mathematical Society. 61, 1481–1507 (2024). https://doi.org/10.4134/BKMS.b230385 CR - Kemajou Mbiakop, T., Ngakeu, F.: Null hypersurface normalized by the structure vector field in a para-Sasakian manifold. International Journal of Maps in Mathematics. 8(1), 85-105 (2025). CR - Navarro, M., Palmas, O., Solis, D. A.: Null screen quasi-conformal hypersurfaces in semi-Riemannian manifolds and applications. Mathematische Nachrichten, 293(8), 1534-1553 (2020). https://doi.org/10.1002/mana.201800494 CR - Ngakeu, F., Djomako, A. C., Ndombol, B.: Rigged null hypersurfaces in almost paracontact metric manifolds. Gulf Journal of Mathematics. 7(2), (2019). https://doi.org/10.56947/gjom.v7i2.190 CR - Perktas, S. Y., Kilic, E., Acet, B. E.: Lightlike hypersurfaces of a para-Sasakian space form. Gulf Journal of Mathematics. 2(2),(2014). https://doi.org/10.56947/gjom.v2i2.194 CR - Zamkovoy, S.: Canonical connections on paracontact manifolds. Annals of Global Analysis and Geometry, 36(1), 37-60 (2009). https://doi.org/10.1007/s10455-008-9147-3 UR - https://doi.org/10.36890/iejg.1611755 L1 - https://dergipark.org.tr/en/download/article-file/4485989 ER -