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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