You probably know by now that a differential k-form k $\ge$ 1 on a domain D is very similar to a vector field on D, and hence a correspondence between the two may be established.Let = F dx + G dy + H dz be a differential 1-form on a domain D and let be the vector field corresponding to . Using this set up, find the vector differential identity corresponding to the fact = .
A) $\bigtriangledown$ (div
F) = 0
B) curl(
F) = 0
C) div(curl
F)= 0
D) F = 0
E) curl(curl
F) = 0

Question

You probably know by now that a differential k-form k $\ge$ 1 on a domain D    is very similar to a vector field on D, and hence a correspondence between the two may be established.Let  = F dx + G dy + H dz be a differential 1-form on a domain D    and let  be the vector field corresponding to  . Using this set up, find the vector differential identity corresponding to the fact    =  .
A) $\bigtriangledown$ (div
F) = 0 
B) curl(
F) = 0 
C) div(curl 
F)= 0 
D) F = 0 
E) curl(curl 
F) = 0

Quizplus · Accepted Answer

The Answer of You probably know by now that a differential k-form k $\ge$ 1 on a domain D    is very similar to a vector field on D, and hence a correspondence between the two may be established.Let  = F dx + G dy + H dz be a differential 1-form on a domain D    and let  be the vector field corresponding to  . Using this set up, find the vector differential identity corresponding to the fact    =  .
A) $\bigtriangledown$ (div
F) = 0 
B) curl(
F) = 0 
C) div(curl 
F)= 0 
D) F = 0 
E) curl(curl 
F) = 0

You Probably Know by Now That a Differential K-Form K ≥\ge≥

You Probably Know by Now That a Differential K-Form K $\ge$