Is Jurdjevic's Definition of Differential Forms an Alternative Approach?

[Kreizhn]

Hey,

A quick question. In the definition of a differential form, we normally require that they be sections of the k-th exterior power of the cotangent bundle. However, on page 14 of Jurdjevic's book on http://books.google.ca/books?id=PpZ...6AEwAA#v=onepage&q=differential form&f=false", he defines them simply as sections of the cotangent projection.

Is there a mistake in his notes or does this represent an alternative way of examining differential forms?

 

[zhentil]

His definition is for 1-forms (covectors).

 

[Kreizhn]

Ah, so do you mean to say that a when the "dimension" of the form is omitted, it should be assumed to be a 1-form?

 

[zhentil]

That's not usual, no. I think the author was being sloppy.