Trying to get my head around some basic exterior calculus concepts

  • Thread starter BWV
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  • #1
BWV
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Trying to get my head around some basic exterior calculus concepts


So #1 - 1-form or covector the grad is a covector / 1-form defined as something that combined with a vector takes it to a scalar, for example divergence is a scalar which is the dot-product of a function with its grad (e.g. a 1-form or covector) - correct?


#2 - is there an correspondance between curl and a wedge product? can curl be written as a wedge product?
 

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  • #2
tiny-tim
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Hi BWV! :smile:
#1 - 1-form or covector the grad is a covector / 1-form defined as something that combined with a vector takes it to a scalar, for example divergence is a scalar which is the dot-product of a function with its grad (e.g. a 1-form or covector) - correct?

#2 - is there an correspondance between curl and a wedge product? can curl be written as a wedge product?
#1 - yes! :smile:

#2 - a cross-product of two three-dimensional vectors is a pseudovector, not a vector, and it's a dual 1-form, the dual of the wedge product 2-form …

same with curl (so it can be written as a wedge product starred) :wink:
 

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