We investigate lightlike hypersurfaces of indefinite Sasakian manifolds, tangent to the structure vector field ξ and whose screen distribution is integrable. We prove some results on parallel vector fields and on a leaf of the integrable distribution \(D_{0} \perp \langle\xi\rangle\) of this class. A theorem on a geometrical configuration of the screen distribution is obtained. We show that any totally contact umbilical leaf of a screen integrable distribution of a lightlike hypersurface is an extrinsic sphere.

中文翻译：

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不确定Sasakian流形的屏幕可积轻型超曲面

我们研究了不确定的Sasakian流形的轻型超曲面，该超曲面与结构矢量场ξ相切，并且其屏幕分布是可积分的。我们证明了在平行矢量场和此类的可积分布\（D_ {0} \ perp \ langle \ xi \ rangle \）的叶子上的一些结果。获得关于屏幕分布的几何构造的定理。我们显示，屏幕状可积分分布的屏幕的任何可完全接触的脐叶都是一个外在球体。