- #1

cianfa72

- 1,953

- 215

- TL;DR Summary
- Clarification about differential k-form vs (0,k) tensor field

Hi,

I would like to ask for a clarification about the difference between a differential k-form and a generic (0,k) tensor field.

Take for instance a (non simple) differential 2-form defined on a 2D differential manifold with coordinates ##\{x^{\mu}\}##. It can be assigned as linear combination of terms ##dx^{\mu} \wedge dx^{\nu}## and it is basically a multi-linear application from ##V \times V## to ##\mathbb R## (##V## is the tangent vector space at each point of the 2D manifold). So I think a 2-form is actually just a

Is that right ? Thank you.

I would like to ask for a clarification about the difference between a differential k-form and a generic (0,k) tensor field.

Take for instance a (non simple) differential 2-form defined on a 2D differential manifold with coordinates ##\{x^{\mu}\}##. It can be assigned as linear combination of terms ##dx^{\mu} \wedge dx^{\nu}## and it is basically a multi-linear application from ##V \times V## to ##\mathbb R## (##V## is the tangent vector space at each point of the 2D manifold). So I think a 2-form is actually just a

*particular*(0,2) tensor field defined on the 2D manifold.Is that right ? Thank you.

Last edited: