## Relatório de pesquisa 29/09

Stochastic Characterization of Harmonic Sections and a Liouville Theorem, Simão Stelmastchuk, submitted October 22, 2009.

Abstract
Let $P(M,G)$ be a principal fiber bundle and $E(M,N,G, P)$ be an associate fiber bundle. Our interest is to study harmonic sections of the projection $\pi_E$ of $E$ into $M$. Our first purpose is to give a stochastic characterization of harmonic section from $M$ into $E$ and a geometric characterization of harmonic sections with respect to its equivariant lift. The second purpose is to show a version of Liouville theorem for harmonic sections and to prove that section $M$ into $E$ is a harmonic section if and only if it is parallel.

Mathematics Subject Classifications (2000):  53C43, 55R10, 58E20, 58J65, 60H30.

Keywords:
harmonic sections; fiber bundles; Liouville theorem, stochastic analisys on manifolds.

Copy of the file:

rp29-09.pdf (PDF)

October 23, 2009

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