Fields in nonaffine bundles. II. Gauge-coupled generalization of harmonic mappings and their Bunting identities

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Abstract
The general-purpose bitensorially gauge-covariant differentiation procedure set up in the preceding article is specialized to the particular case of bundles with nonlinear fibers that are endowed with a (torsion-free) Riemannian or pseudo-Riemannian metric structure. This formalism is used to generalize the class of harmonic mappings between Riemannian or pseudo-Riemannian spaces to a natural gauge-coupled extension in the form of a class of field sections of a bundle having the original image space as fiber, with a nonintegrable gauge connection A belonging to the algebra of the isometry group of the fiber space. The Bunting identity that can be used for establishing uniqueness in the strictly positive metric-Riemannian case with negative image-space curvature is shown to be generalizable to this gauge-coupled extension.
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