A Reeb component in dimension 3 is a solid torus equipped with a codimension-one foliation
whose boundary torus is a foliation
leaf and whose interior foliation
leaves are planes that accumulate on the boundary (Calegari
2007, p. 144). The Reeb foliation of the hypersphere 
is obtained by gluing two such components along their boundary.
A foliation which has no Reeb components is said to
be Reebless.
Reeb Component
See also
Foliation, Foliation Leaf, Generalized Reeb Component, Reeb FoliationPortions of this entry contributed by Christopher Stover
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References
Calegari, D. Foliations and the Geometry of 3-Manifolds. Oxford, England: Clarendon Press, p. 144, 2007.Imanishi, H. and Yagi, K. "On Reeb Components." J. Math. Kyoto Univ. 16, 313-324, 1976.Referenced on Wolfram|Alpha
Reeb ComponentCite this as:
Weisstein, Eric W., with contributions by Christopher Stover. "Reeb Component." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ReebComponent.html