I read that for the Levi-Civita symbol $\tilde{\epsilon}_{ijk}$, people somtimes define another version of the symbol with upper indices: $$\tilde{\epsilon}^{ijk}=\text{sgn} (g) \tilde{\epsilon}_{ijk} $$ where $\text{sgn}(g)$ is the sign of the metric determinant. How is $\text{sgn}(g)$ computed?

  • 2
    $\begingroup$ en.wikipedia.org/wiki/Sign_function. It's also handy to know the different conventions adopted by authors: see here $\endgroup$ Mar 16, 2021 at 6:31
  • $\begingroup$ Do you know how the metric determinant is defined? $\endgroup$
    – Filippo
    Mar 16, 2021 at 6:51
  • $\begingroup$ @NiharKarve Thank you. Very useful. $\endgroup$
    – TaeNyFan
    Mar 16, 2021 at 7:50


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