This article is cited in 2 papers

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

S. E. Stepanov

Vladimir State Pedagogical University

Abstract: 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.

UDC: 514.763.2

Received: 01.11.1997

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