Hi everyone,(adsbygoogle = window.adsbygoogle || []).push({});

I'm having difficulty with an exercise I have to do in differential geometry this semester. Suppose that the interior product (also known as the interior derivative) is denoted by [tex] i_X [/tex]. Then the exercise is to show that:

[tex] i_X\star\omega = \omega\wedge X^\flat [/tex]

where [tex] X^\flat [/tex] is the 1-form related to [tex] X [/tex] by the metric and the star is the Hodge Star dual operator.

The problem is I don't really know where to start. I've tried several approaches, for example taking the interior derivative of [tex] \phi\wedge\star\omega [/tex] where [tex] \phi [/tex] is a p-form, and using the defining property of the star operator, but I can't see it leading anywhere.

Any suggestions?

Kane O'Donnell

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

Dismiss Notice

Join Physics Forums Today!

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

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

# Hodge Duals and the Interior Product

Loading...

Similar Threads for Hodge Duals Interior | Date |
---|---|

Existence of Hodge Dual: obvious or non-trivial? | Feb 18, 2014 |

Wedge products and Hodge dual | Jul 27, 2013 |

How to make a hodge dual with no metric, only volume form | Feb 10, 2011 |

Tensor components of a Hodge dual | Dec 2, 2008 |

A simple derivation involving the Hodge dual | Jul 2, 2007 |

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