  This paper introduces $\anabla$-tensors on lightlike hypersurfaces $M^{n+1}$
of signature $(0,n)$, $(n\geq 1)$ and investigates on their properties in
connection with the null geometry of $M$. In particular, we show that there is
an interplay between existence of $\anabla$-tensors of certain type and
lightlike warped product structures.
