Base Manifold

The base manifold in a bundle is analogous to the domain for a set of functions. In fact, a bundle, by definition, comes with a map to the base manifold, often called pi or projection.

For example, the base manifold to the tangent bundle of a manifold M is the manifold M. A vector field is a function from the manifold to the tangent bundle, with the restriction that every point gets mapped to a vector at that point. In general, a bundle has bundle sections, at least locally, which are maps from the base manifold to the bundle.

See also

Bundle, Bundle Section, Manifold, Tangent Bundle, Vector Bundle

This entry contributed by Todd Rowland

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Rowland, Todd. "Base Manifold." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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