On an application of the Stokes' theorem in global Riemannian geometry

Applying the Stokes' theorem we have deduced the Weitzenbock's formula for symmetric 2-forms on a compact Riemannian manifold $M$ with boundary $\partial M\neq\varnothing$. Using the formula we have proved that Killing symmetric 2-forms and Killing $p$-forms on a Riemannian manifold $M$ of non-positive sectional curvature and convex boundary $\partial M$ must be either parallel or zero. Finally, we have applied our results to the global theory of projective and umbilical maps.