What is a de Rham k-form?

Question

I generally know what a differential k-form is. But what does it mean for a k-form to be a "de Rham" k-form?

Thanks in advance!

Answer 1

A "de-Rahm k-form" is an equivalence class of closed k-forms where two closed k-forms are in the same equivalence class if their difference is an exact k-form. But usually when dealing with equivalence classes you work in practice with a representative of that class, so a de-Rahm k-form will probably mean in your case some representative of such an equivalence class.