“Reeb foliation”的意思、由来-开放百科全书

词条

Reeb foliation

释义

Illustrations
References
External links

In mathematics, the Reeb foliation is a particular foliation of the 3-sphere, introduced by the French mathematician Georges Reeb (1920–1993).

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.

By Novikov's compact leaf theorem, every smooth foliation of the 3-sphere includes a compact torus leaf, bounding a solid torus foliated in the same way.

Illustrations

References

{{cite book | author=G. Reeb | title=Sur certaines propriétés topologiques des variétés feuillétées | series=Actualités Sci. Indust. | volume=1183 | publisher=Hermann | location=Paris | year=1952 }}
{{cite book | title=Foliations | author=Alberto Candel |author2=Lawrence Conlon | publisher=American Mathematical Society | year=2000 | isbn=0-8218-0809-5 | page=93 }}
{{cite book | title=Introduction to Foliations and Lie Groupoids | author=Ieke Moerdijk |author2=J. Mrčun | series=Cambridge studies in advanced mathematics | volume=91 | publisher=Cambridge University Press | year=2003 | isbn=0-521-83197-0 | page=8 }}

External links

{{MathWorld|urlname=ReebFoliation|title=Reeb Foliation}}

1 : Foliations

随便看

开放百科全书收录14589846条英语、德语、日语等多语种百科知识，基本涵盖了大多数领域的百科知识，是一部内容自由、开放的电子版国际百科全书。