$delta (2)$-ideal euclidean hypersurfaces of null $l_1$-2-type

We say that an isometric immersion hypersurface $ x:m^nrightarrowmathbb{e}^{n+1}$ is ofnull $l_k$-2-type if $x =x_1+x_2$, $ x_1, x_2:m^nrightarrowmathbb{e}^{n+1}$ are smooth maps and $l_k x_1 =0, ~ l_k x_2 =lambda x_2$, $lambda$ is non-zero real number, $l_k$ is the linearized operator ofthe $(k + 1)$th mean curvature of the hypersurface, i.e., $l_k( f ) =text{tr} (p_k circ text{hessian} f )$ for$f in c^infty(m)$, where $p_k$ is the $k$th newton transformation, $l_k x = (l_k x_1, ldots , l_k x_{n+1}), ~x = (x_1, ldots, x_{n+1})$. in this article, we classify $delta (2)$-idealeuclidean hypersurfaces of null $l_1$-2-type