differential form to vector field and back

asked 2018-01-27 12:46:21 +0100

629 ●9 ●27 ●40

Is there a way to convert a vector field into a corresponding differential 1-form (work form) or a corresponding differential 2-form (flow form)?

And vice versa, is there a way to convert a 1-form or a 2-form into a corresponding vector field?

Thanks.

answered 2018-01-27 14:28:11 +0100

eric_g
8424 ●10 ●62 ●166 https://luth.obspm.fr/...

Yes, but you need a metric for this. If the metric is g, then to transform a vector field v into a 1-form, it suffices to write

v.down(g)

while to transform a 1-form f into a vector field, the command is

f.up(g)

More details in this section of the reference manual.

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Comments

Thanks Eric.

What about the flux form .i.e. converting a vector field into its corresponding 2-form and back? As you mentioned above, this depends on the metric `g

Daniel

danielvolinski ( 2018-01-27 21:57:42 +0100 )edit

In dimension 3, you can get the flux 2-form as the Hodge dual of the 1-form associated to the vector:

v.down(g).hodge_dual(g)

More details here.

eric_g ( 2018-01-27 23:42:55 +0100 )edit

Thanks Eric

danielvolinski ( 2018-03-15 12:46:20 +0100 )edit

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