In our discussion of vector bundles, we put no greater structure on the fibers than that of topological vector space (of the same category as those used to build up manifolds). One can strengthen the notion so as to include the metric structure, and we are thus led to consider Hilbert bundles, whose fibers are Hilbert spaces.
KeywordsHilbert Space Vector Bundle Topological Vector Space Tubular Neighborhood Riemannian Metrics
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