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The Einstein 3-form \(G_\alpha\) and its equivalent 1-form \(L_\alpha\) in Riemann-Cartan space. (English) Zbl 0989.83005
The author starts with a (local) coframe in an \(n\)-dimensional differentiable manifold endowed with a linear connection; using the Bianchi identities, he constructs a curvature dependent \((n-1)\)-form, called the Einstein form and some “dual” 1-form \(L\). Properties of these two forms are established, together with new interpretations of known formulae (Einstein’s field equation, Salgado’s formula). Particularizations in the metric (pseudo-Riemannian) framework are also given.
The reviewer considers that a coordinate-free expression of these interesting constructions would lead to a better insight of the global manifold invariants involved.

83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
53B05 Linear and affine connections
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
58A10 Differential forms in global analysis
Full Text: DOI
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