Reeb foliation

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In mathematics, the Reeb foliation is a particular foliation of the 3-sphere, introduced by the French mathematician Georges Reeb (1920–1992).

It is based on dividing the sphere into two solid tori, along a 2-torus: see Clifford torus. Each of the solid tori is then foliated internally, in codimension 1, and the dividing torus surface forms one more leaf.

Illustrations

2-dimensional section of Reeb foliation
3-dimensional model of Reeb foliation

References

  • G. Reeb (1952). Sur certaines propriétés toplogiques des variétés feuillétées. Actualités Sci. Indust. 1183. Paris: Hermann. 
  • Alberto Candel; Lawrence Conlon (2000). Foliations. American Mathematical Society. p. 93. ISBN 0-8218-0809-5. 
  • Ieke Moerdijk; J. Mrcun (2003). Introduction to Foliations and Lie Groupoids. Cambridge studies in advanced mathematics 91. Cambridge University Press. p. 8. ISBN 0-521-83197-0. 

External links

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