Hello! My teacher told me that the description of this example is not 100% correct. Here is the example

http://i51.tinypic.com/34dihx5.jpg

but my teacher says that f is not a 2-form, it is a Hodge * -dual to 1-form and when we write that f is the rotation than it should mean that f=dw which is not true in this case.

Does anyone know who is right? and where is the eventual error?

thanks