I read a problem a while ago which was to find a differential form on the circle which is not the differential of any function. Being a hapless physicist, this puzzled me for a while. I've found an answer in Spivak's Calculus on Manifolds, but I need a little help in following his reasoning.(adsbygoogle = window.adsbygoogle || []).push({});

He argues that the form [tex]d\theta[/tex] is such a form, and shows that if it is the differential of a function [tex]f[/tex] then [tex]f = \theta + constant[/tex]. I am OK up to this point, but I fail to see how such an [tex]f[/tex] can't exist, like he argues.

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Forms on the circle

Loading...

Similar Threads - Forms circle | Date |
---|---|

I Some Question on Differential Forms and Their Meaningfulness | Feb 19, 2018 |

A Exterior forms in wiki page | Dec 22, 2017 |

I Integration of a one form | Nov 5, 2017 |

I Maurer-Cartan form | Nov 2, 2017 |

Similar triangles formed by the diagonals of a quadrilateral inscribed in a circle | Mar 4, 2009 |

**Physics Forums - The Fusion of Science and Community**