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differential form to vector field and back

asked 2018-01-27 05:46:21 -0500

danielvolinski gravatar image

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.

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answered 2018-01-27 07:28:11 -0500

eric_g gravatar image

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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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 gravatar imagedanielvolinski ( 2018-01-27 14:57:42 -0500 )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 gravatar imageeric_g ( 2018-01-27 16:42:55 -0500 )edit

Thanks Eric

danielvolinski gravatar imagedanielvolinski ( 2018-03-15 06:46:20 -0500 )edit

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Asked: 2018-01-27 05:46:21 -0500

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Last updated: Jan 27