Foliations of the Plane

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1 total messages Started by Daniel A. Asimov Wed, 16 Dec 1992 20:44

#167

Author: Daniel A. Asimov
Date: Wed, 16 Dec 1992 20:44

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Let F denote a smooth foliation of R^2.  

Does there necessarily exist a C^1 function g: R^2 -> R such that each 
leaf of F is a connected component of a level set of g ?  

If this is always possible, can g always be chosen so as to also be smooth?


Dan Asimov
Mail Stop T045-1
NASA Ames Research Center
Moffett Field, CA 94035-1000

asimov@nas.nasa.gov
(415) 604-4799

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