An identity in Riemann–Cartan geometry

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Abstract

We derive a new Gauss–Bonnet type identity in Riemann-Cartan geometry: (−g)1/2εμνλρ (Rμνλρ + (1/2) CαμνCαλν) = ∂μ (−(−g)1/2εμνλρCμνλρ), where Cαμν is the torsion tensor.

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Nieh et al. (Mon,) studied this question.

synapsesocial.com/papers/6a110bb3cd70b138bf1a15bc https://doi.org/https://doi.org/10.1063/1.525379