Geodesic
On an application of the Stokes' theorem in global Riemannian geometry
Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 1, pp. 245-262

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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. 
@article{FPM_2002_8_1_a17,
     author = {S. E. Stepanov},
     title = {On an application of the {Stokes'} theorem in global {Riemannian} geometry},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {245--262},
     publisher = {mathdoc},
     volume = {8},
     number = {1},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2002_8_1_a17/}
}
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S. E. Stepanov. On an application of the Stokes' theorem in global Riemannian geometry. Fundamentalʹnaâ i prikladnaâ matematika, Tome 8 (2002) no. 1, pp. 245-262. http://geodesic.mathdoc.fr/item/FPM_2002_8_1_a17/