📢Vanishing Divergence of the Levi-Civita Tensor Explained

The totally antisymmetric tensor, is a true tensor formed by dividing the Levi-Civita symbol. Its divergence vanishes identically because it is covariantly constant, a fundamental property of the Levi-Civita connection that preserves the volume element. The explicit proof requires recognizing the identity, which combined with the hint formula, demonstrates that the two non-vanishing terms in the covariant derivative perfectly cancel each other out.

Vanishing Divergence of the Levi-Civita Tensor | Proof and Derivationviadean on Notion