FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2002, VOLUME 8, NUMBER 1, PAGES 245-262

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

S. E. Stepanov

Abstract

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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 $$¶M ¹ Æ.
Using the formula we have proved that Killing symmetric
$2$-forms and
Killing $p$-forms
on a Riemannian manifold $M$ of non-positive sectional
curvature and convex boundary $$¶M
must be either parallel or zero.
Finally, we have applied our results to the global theory of
projective and umbilical maps.

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Location: http://mech.math.msu.su/~fpm/eng/k02/k021/k02118h.htm

Last modified: July 8, 2002