Differential Identities in Einstein Nonsymmetric Geometry
Abstract
We derive differential identities in the domain of Einstein nonsymmetric geometry. We introduce a local form of the nonsymmetric linear connection of a totally skew-symmetric torsion, which has been constructed and published in a global form in a previous work. The local form of this connection is expressed in terms of the symmetric and skew-symmetric parts of the nonsymmetric metric tensor as well as their derivatives. We apply the Dolan–McCrea variational scheme using a nonsymmetric metric tensor $$G_{\mu\nu}$$ . We demonstrate our rigorous proof via analyzing the generalized second-order metric tensor $$G_{\mu\nu}$$ to its symmetric and skew-symmetric parts, respectively. The derived differential identities can be split into two differential identities such that one identity is expressed in terms of the symmetric part of $$G_{\mu\nu}$$ , and the second one in terms of the skew part of $$G_{\mu\nu}$$ . One of the demonstrated differential identities can be considered as a generalization of the second Bianchi identity. This identity is reduced to the conventional Riemannian one in the case of using the Ricci scalar.
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How to cite
Wanas, M. I., Nabil, S., Abdelhamid, N. E., & ElAbd, K. (2025). Differential Identities in Einstein Nonsymmetric Geometry. Gravitation and Cosmology, 31(2), 185–194. https://doi.org/10.1134/s0202289325700070