Flux coordinates: Difference between revisions
| Line 41: | Line 41: | ||
g^j_i | g^j_i | ||
= \mathbf{e}_i\cdot\mathbf{e}^j = \delta_i^j ~. | = \mathbf{e}_i\cdot\mathbf{e}^j = \delta_i^j ~. | ||
</math> | |||
The metric tensors can be used to ''raise'' or ''lower'' indices. Take | |||
:<math> | |||
\mathbf{B} | |||
= B_i\mathbf{e}^i = B_i g^{ij}\mathbf{e}_j = B^j\mathbf{e}_j~, | |||
</math> | |||
so that | |||
:<math> | |||
B^j = g^{ij} B_i~. | |||
</math> | </math> | ||