Address: Departamento de Matemática, Universidade Estadual do Paraná, 84600-000 – União da Vitória - PR, Brazil
E-mail: simnaos@gmail.com
Abstract: Let $P(M,G)$ be a principal fiber bundle and $E(M,N,G,P)$ an associated fiber bundle. Our interest is to study the harmonic sections of the projection $\pi _{E}$ of $E$ into $M$. Our first purpose is give a characterization of harmonic sections of $M$ into $E$ regarding its equivariant lift. The second purpose is to show a version of a Liouville theorem for harmonic sections of $\pi _{E}$.
AMSclassification: primary 53C43; secondary 55R10, 58E20, 58J65, 60H30.
Keywords: harmonic sections, Liouville theorem, stochastic analysis on manifolds.
DOI: 10.5817/AM2012-2-149