A one-form versus a dual basis vector

[Scott4775]

Hi everyone,

Pardon the neophyte question, but is a one-form the same thing as a dual basis vector? If not, are they related in some way, or completely different concepts/entities?

Thank you!

 

[Mentz114]

Welcome to PF.

The dual basis vectors are 1-forms, but not all 1-forms are dual basis vectors. In fact given a set of dual basis vectors we can construct any number of 1-forms.

 

[elfmotat]

Dual basis vectors are to one-forms as basis vectors are to vectors.