A circle bundle is a fiber bundle whose fibers are circles. It may also have the structure of a principal bundle if there is an action of that preserves the fibers, and is locally trivial. That is, if every point has a trivialization such that the action of on is the usual one.
Circle Bundle
See also
Bundle, Group Action, Principal BundleThis entry contributed by Todd Rowland
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Rowland, Todd. "Circle Bundle." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/CircleBundle.html