Flux coordinates: Difference between revisions

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while the curl is  
while the curl is  
:<math>
:<math>
  \nabla\times\mathbf{A} = \frac{\varepsilon_{ijk}}{\sqrt{g}}\frac{\partial}{\partial u^i}(\sqrt{g}A_j)\mathbf{e}_k \Rightarrow
  \nabla\times\mathbf{A} = \frac{\varepsilon_{ijk}}{\sqrt{g}}\frac{\partial A_j}{\partial u^i}\mathbf{e}_k \Rightarrow
\left(\nabla\times\mathbf{A}\right)^k = \frac{\varepsilon_{ijk}}{\sqrt{g}}\frac{\partial}{\partial u^i}(\sqrt{g}A_j)
\left(\nabla\times\mathbf{A}\right)^k = \frac{\varepsilon_{ijk}}{\sqrt{g}}\frac{\partial A_j}{\partial u^i}
</math>
</math>
given in terms of the covariant base vectors, where <math>\varepsilon_{ijk}</math> is the [[::Wikipedia:Levi-Civita symbol| Levi-Civita]] symbol.
given in terms of the covariant base vectors, where <math>\varepsilon_{ijk}</math> is the [[::Wikipedia:Levi-Civita symbol| Levi-Civita]] symbol.
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