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Flux coordinates: Difference between revisions
→Coordinates and basis vectors
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\mathbf{e}_i\cdot\mathbf{e}^j | \mathbf{e}_i\cdot\mathbf{e}^j | ||
= \delta_{i}^{j} \to \mathbf{e}_i | = \delta_{i}^{j} \to \mathbf{e}_i | ||
= \frac{\mathbf{e}^j\times\mathbf{e}^k}{ | = \frac{\mathbf{e}^j\times\mathbf{e}^k}{\mathbf{e}^i\cdot\mathbf{e}^j\times\mathbf{e}^k} | ||
= \sqrt{g}\;\mathbf{e}^j\times\mathbf{e}^k ~, | = \sqrt{g}\;\mathbf{e}^j\times\mathbf{e}^k ~, | ||
</math> | </math> | ||