In this paper, we investigate a complete noncompact submanifold
![$ M^m$](img34.png)
in a hyperbolic space
![$ H^{m+t}(-1)$](img35.png)
. For
![$ p$](img33.png)
-harmonic 1-forms, we obtain a vanishing and finiteness theorem under the assumptions on Schrödinger operators involving the squared norm of the traceless second fundamental form.