- #1

Baela

- 17

- 2

\begin{align}

g_{mn}\epsilon^{npqr}=\epsilon_{m}{}^{pqr}

\end{align}

where ##g_{mn}## is the metric and ##\epsilon^{npqr}## is the Levi-Civita tensor.

The Levi-Civita symbol, which we can denote by ##\varepsilon^{npqr}##, is not a tensor. It obeys the relation

\begin{align}

\varepsilon^{npqr}=\varepsilon_{npqr}.

\end{align}

What happens if the metric tensor is multiplied with the Levi-Civita symbol ##\varepsilon^{npqr}##?

\begin{align}

g_{mn}\varepsilon^{npqr}=\,?

\end{align}