Regularity of weakly harmonic sections of a fiber bundle and Gauss sections

摘要

We study the regularity of weakly harmonic sections of fiber bundles (N, M, π), where (M, g) and (N, h) are Riemannian manifolds. One of our results is that, when the fibers are regular geodesic balls and the fiber bundle is Riemannian, any weakly harmonic section is continuous. We also study the existence and regularity of harmonic Gauss sections with application to foliations.